Stock Valuation & Data collection

Figure 1. Simple Valuation Spreadsheet

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Computerized Investing > January 2011

A Simple Valuation Spreadsheet Many individual investors view individual stock analysis and selection as a daunting task. However, the process can be made easier by organizing the decision­making process to ensure that pertinent data and information are evaluated in a logical sequence so that the investor can arrive at a reasonable and thoughtful decision.

The ultimate goal of fundamental analysis is to determine, using a variety of variables, what you think a stock is really worth and comparing that estimated value to the stock’s current stock price. This way you can gain an insight into whether the stock is undervalued, overvalued or fairly valued.

This installment of the Spreadsheet Corner introduces a simple valuation spreadsheet from AAII’s book “Stock Investing Strategies,” by Maria Crawford Scott and John Bajkowski. This spreadsheet provides an easy­to­follow, systematic format that walks you through the complete process of arriving at a value for a stock without getting bogged down in complicated financial formulas and analysis. AAII members can download a free electronic copy of the book from the Investment E­books segment of the Getting Started area of AAII.com (www.aaii.com/investing­basics/investment­ebooks). You can download the Simple Valuation Spreadsheet from the online version of this article at the Computerized Investing website, as well as from the Spreadsheets section of the AAII Download Library (www.aaii.com/download­library/results?Category=SS).

The Valuation Spreadsheet

The Simple Valuation Spreadsheet, shown in Figure 1, contains two valuation models at the bottom. One is based on a firm’s earnings and the other on its dividends.

The underlying formulas for the two models look different, but they are actually quite similar. They equate a stock’s price to a stream of future earnings or dividends by asking the question: How much are investors willing to pay now for these future expected streams?

Both models make the key assumption that the growth prospects of the firm will not change fundamentally over time. Relying on this assumption, we can use the historical relationships between the stock’s price and its

 

 

To download the Excel Spreadsheet, click here.

earnings or dividends to estimate future values. If current market prices differ significantly from the estimated value based on these historical relationships, it means that the market—for whatever reason—is evaluating future income potential differently and may be mispricing the stock.

Earnings Model

The first model at the bottom of the valuation spreadsheet is geared toward stocks with low or

non­existent dividends—the traditional “growth” stock—and is a price­earnings ratio (P/E) approach.

The price­earnings ratio (share price divided by earnings per share over the last 12 months) indicates how much investors are willing to pay for each dollar of a firm’s earnings. The higher the price­earnings ratio—the more investors are paying for earnings—the more confident investors are about the expected future earnings. Conversely, lower ratios indicate low earnings expectations, or a low confidence in earnings predictability.

For the earnings valuation, the average annual high and low price­earnings ratios are calculated for prior years. Multiplying these historical ranges by an estimate of next year’s earnings per share provides an estimate of future value.

While it may seem difficult to make an earnings estimate, the recent earnings history that is part of the worksheet will give you some basis for forming those expectations. In addition, there are a number of sources where you can obtain analysts’ estimates of future earnings, including Morningstar.com, Reuters.com, Yahoo! Finance and Zacks.com.

Dividend Model

The second valuation model in this worksheet is primarily for mature, dividend­paying stocks, which tend to be low­growth stocks. As such, it is a dividend yield approach. Dividend yield—annual dividends per share divided by share price—is the annual dividend as a percentage of the current stock price. In other words, it relates share price to dividends: the lower the dividend yield, the greater the company’s emphasis on earnings growth and the greater the disregard for dividend income. The higher the dividend yield, the lower the expectation among investors of earnings growth; instead there is a greater emphasis on dividend income. At the extreme, a high dividend yield may indicate the expectation of a dividend decrease.

This approach requires an estimate of the next expected annual cash dividend. Again, the recent dividend history in the worksheet should provide you with a feel for changes over

 

 

time. Also, some services provide the indicated dividend, which is the total projected dividend per share payment over the next 12 months.

Dividing the expected annual dividend by the average low dividend yield will give a high­ price estimate; dividing the expected annual dividend by the average high dividend yield results in the low­price estimate.

Financial Checklist

It’s easy to compare the valuations you come up with to the current market price. But those valuations are only as good as the inputs and assumptions used in formulating the models.

For instance, the models assume that the firm’s growth prospects have not fundamentally changed. But will growth continue at its current pace? The models also assume that historical relationships will continue. But were past relationships affected by a one­time occurrence that is unlikely to continue? Will dividends continue to be paid at the same rate?

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Examining the historical patterns of the per share figures and ratios, and comparing them to competitors and industry and market benchmarks, is particularly useful in evaluating your inputs and assumptions.

Have earnings grown at a stable rate? Have the earnings per share been steady and positive each year, or have they been volatile, making predictions more difficult? For dividend­paying firms, has the payout ratio been steady? Increases in the payout ratio, and payout ratios above 100%, are an indication that future dividends may go

 

 

Figure 2. Kellogg Data on Morningstar.com

down; high payout ratios mean slower or no dividend growth, and perhaps even a decline. Is the current price­earnings ratio low relative to the market, the industry or a competitor, and does this vary from previous years? Is the current dividend yield high relative to the market, the industry or a competitor, and does this vary from previous years? Has the return on equity, an indication of how well the firm has used reinvested earnings to generate additional earnings, been high and stable? Is the use of financial leverage, a measure of financial risk that indicates how much of the firm’s assets have been financed by debt, low relative to industry norms?

Sources of Data

Thus far our discussion has focused on the bottom portion of the spreadsheet—the valuation models that help you find stocks that are potentially undervalued or overvalued based on their earnings and dividend histories.

However, in order to arrive at these valuations, you need to fill out the top portion of the spreadsheet. This section—the Financial Statement and Ratio Analysis—organizes the information needed for the valuation models and provides figures that serve as a financial checklist for your analysis. Here you can analyze the assumptions underlying the valuation models; this is important, because if these assumptions are wrong, your valuations will be flawed.

You have several options for collecting the underlying data to populate this spreadsheet. Luckily, filling in the yellow­highlighted cells is the only legwork you need to do, as this spreadsheet calculates the ratios and valuations for you.

The first section indicates per share information regarding the stock—the high and low prices for each of the last five years, as well as earnings per share and dividends per share figures for each of the last five years (moving from left to right, the Year 1 column contains the most recent figures and the Year 5 column contains the oldest figures).

Price Data

Using a free site such as Morningstar.com, you can find the high and low prices of a company on an annual basis. Figure 2 shows the annual price history for Kellogg Company (K) from the start of 2005 through the end of 2009. Interestingly enough, however, we found a data error at the Morningstar site. While the site claimed that the high price for K

 

 

Figure 3. Kellogg Data on SmartMoney.com

shares in 2006 was $57, we could not find another supporting source. Instead, we found multiple stock charts that pegged the high price for that year at $50.95, which is what we used for our analysis.

Earnings and Dividends

After entering in the high and low prices for the last five years, the next step is to locate the annual earnings per share and dividends per share figures, also for each of the last five years. The “Financials” section of Morningstar.com provides five years of financial statement data for free. While, from a time­saving standpoint, it is convenient to find the necessary data from a single source, another excellent site for financial statement data is SmartMoney.com. Here you will find up to 10 years of annual data and 15 quarters of quarterly data. Figure 3 shows the annual financial data for Kellogg over the last five years.

Using the historical earnings and dividends data, we can calculate five­year growth rates for both. The equation built into this valuation spreadsheet to calculate the growth rate of earnings per share (EPS) and dividends per share (DPS) is as follows:

[(Y1 ÷ Y5) 1/n – 1.00] = g

Where:

Y1 = latest EPS or DPS value

Y5 = earliest EPS or DPS value

n = number of annual compounding periods  g = growth rate (%)

Note that with five years of data, you will have only four annual compounding periods—Year 5 to Year 4, Year 4 to Year 3, Year 3 to Year 2 and Year 2 to Year 1. Also, this formula only

 

 

works when the beginning and ending values are positive.

Financial Ratios

The next section of the valuation worksheet lists financial ratios, specifically two primary multiples—price earnings ratio and dividend yield. For the valuation models, these two figures are calculated from the per share data. For the price­earnings ratios, the spreadsheet divides the high and low prices by earnings per share for the same year. For dividend yield, the annual cash dividends per share payments are divided by the low and high price for the same year. The spreadsheet arrives at the five­year averages by adding the yearly figures and dividing the sum by five. If earnings are negative in a given year, or if dividends are nonexistent, the spreadsheet will return an “na” value for that year. In this case, you will need to adjust the divisor in column H to reflect the number of years with a valid earnings or dividend value.

Also included in this spreadsheet is the payout ratio (dividends per share divided by earnings per share), return on equity (earnings per share divided by book value per share), and financial leverage [such as long­term debt to equity or long­term debt to capitalization (long­term debt plus equity)], which are used as part of your financial checklist. Most of these ratios can be calculated from the per share financial data in this worksheet, or they can be taken from stock information sources. Financial leverage cannot be calculated by the per share data in this worksheet, and various sources use different measures. Again, Morningstar.com offers five years of financial leverage (assets to equity) and debt­to­equity data for free.

Financial ratios for the industry in which the firm operates (or for a close competitor), as well as for the market as a whole, are part of the checklist. Unfortunately, it is becoming more difficult to find multiple years of historical financial data and sector/industry/market data all at the same site, for free. Morningstar.com and Reuters.com are two sites that do offer this comparative data for a more complete company analysis.

Are Figures Reasonable?

For this article we used Kellogg Company, the Michigan­based cereal and snack maker, to illustrate the use of this simple worksheet. We used data available for free to supply the data required for this spreadsheet (those cells in Figure 1 highlighted in yellow).

Plugging these numbers into the valuation models, you see that the price­earnings ratio model determines a high price of $66.34 (cell I30) and a low price of $52.54 (cell I32) for an average price of $59.44, while the dividend model produces a high of $67.19 (cell I35) and a low of $51.74 (cell I37) for an average price of $59.47. [You may end up with slightly different numbers due to rounding.] The current price is around $50: It’s trading slightly below the predicted range of both the price­earnings model and the yield­based model.

 

 

Are the assumptions and figures used in the model reasonable? A run through the checklist evaluates this:

Yearly earnings per share appear to be increasing in a fairly stable pattern, and all of the figures were positive. Morningstar’s earnings estimates for the current fiscal year of $3.58 per share and $4.10 per share for the next fiscal year indicate that this trend is expected to continue. This signals earnings growth over the next two years that is almost double that of the last five years. Further analysis would be useful to determine whether or not you agree with Morningstar’s assessment. Had we used Morningstar’s earnings estimates for Year 6 ($3.58), we would have arrived at a valuation range of $55.34 to $69.86 using the price­earnings model. Kellogg’s payout ratio been relatively stable over the last five years. We were unable to locate an online source for industry norms, so we used AAII’s Stock Investor Pro fundamental stock screening and research database program for the industry payout ratio data. From this data we see that Kellogg’s payout ratio is well above the industry median, or midpoint, value. Further investigation revealed that only about 30% of the companies in the food processing industry pay a dividend, lowering the median value for the overall industry. When comparing the median value of those companies paying a dividend, Kellogg’s payout ratio is in line with its industry counterparts. This indicates that the company should be able to support its dividend payout or even increase the payout if earnings continue to grow. Kellogg’s price­earnings ratio is low compared to its industry. Its dividend yield is roughly equal to the industry average. Kellogg’s return on equity (ROE) has risen over the last five years, although it dropped from Year 2 to Year 1. There was a significant increase from Year 3 to Year 2, as Kellogg appears to have significantly raised its debt load (as shown by the increase in its debt­to­equity ratio, which is what we used to measure financial leverage). The company’s debt­to­equity ratio is significantly higher than the industry average. Companies can boost return on equity by taking on more debt, but they increase their risk to shareholders in the process.

The financial checklist indicates that some of the assumptions in the model are reasonable, but some—such as the assumptions concerning dividend and earnings growth—should be examined in more detail. A higher Year 6 earnings per share estimate would, of course, produce higher valuation estimates.

Conclusion

While this valuation spreadsheet offers a basic framework for analysis, you would need to look at other fundamental aspects of the company before any investment decision is made.

For a simple beginning, the Simple Valuation Spreadsheet will provide you with an easy­to­ follow systematic approach to determining value. The basic format is to:

 

 

Determine which valuation model best suits your needs, Determine what information you need to gather for those valuations, and Determine what information you need in order to evaluate the assumption and other inputs used in the models.

Maria Crawford Scott, former editor of the AAII Journal, John Bajkowski, president of AAII, and Wayne A. Thorp, CFA, editor of Computerized Investing, contributed to this article.

Click here to download spreadsheet.

 

Discussion

Edward from NY posted over 6 years ago:

Is there a spreadsheet that compares different companies Revenue/Employee? Net earnings/employee?

Richard from CA posted over 6 years ago:

Could we get this spreadsheet incorporated into SIPro???

Richard from CA posted over 5 years ago:

Or is the Valuations Tab serving the same function?

Carroll from CA posted over 5 years ago:

Are these evaluations essentially what is used by the various advisors, ie) Standard and Poors, etc? If so, is this exercise merely a duplication of what is already available?

E from GA posted over 5 years ago:

It would be most helpfull if you published the answers to the questions.

 

 

Joesph from PA posted over 5 years ago:

I, like others, are interested in the responses to the above questions. Where can one easily and collectively get the information to propagate/load into the spreadsheet to facilitate analysis?

Fuad Nuwaysir from FL posted over 4 years ago:

After updating Adobe Reader, I tried downloading the book “Stock Investing Strategies,” by Maria Crawford Scott and John Bajkowski.  I get the following message:  “This file is damaged and could not be repaired.”  “Local/EWH#6btt[g”  I hope you are able to repair the damaged file and post it again.  The other two books downloaded without a hitch.  F. Nuwaysir

Joe Lan from IL posted over 4 years ago:

Hi Fuad,

The file is working properly and is not damaged.

Thanks.

Stu from RI posted over 3 years ago:

Can you suggest a site from which you could obtain the historical data listed on this sheet. Can find lots of sites for the current info, but having a real problem finding the past 5 yrs

Sorry, you cannot add comments while on a mobile device or while printing.

© 2017 The American Association of Individual Investors

This content originally appeared in the Computerized Investing

 

Shelly Cashman Word 2019 | Modules 4-7: SAM Capstone Project 1a

COMPANY NAME 

Click to Select A Date

INSERT INSIDE ADDRESS

INSERT GREETING LINE

The past year was exceptionally productive for Hankins Aerospace as we increased profitability and established a foundation for the future through sustainable growth and continued excellence in our products and services.

We remain committed to our mission of improving the performance and integrity of aerospace parts and systems. We are equally committed to our shareholders, customers, employees, their families, and the world around us.

To summarize the highlights of the enclosed report, consolidated sales in the past year were $895 million, an increase of 12 percent from the previous year. The company generated $108 million in cash flow, with 45 percent of that returning to shareholders. Since we began paying dividends 10 years ago, annual dividends have increased 210 percent.

As a shareholder in Hankins Aerospace since [YEAR], you are a valuable member of the Hankins team. Through your investment, you have made our success possible. We are dedicated to the integrity, innovation, leadership, and hard work that has earned your confidence so far. We will continue to follow these principles as we strive to meet our goals.

Sincerely,

Louis Feeney

President and Chief Executive Officer

[insert email address]

enc.

Strategic Growth and Advanced Technology

The market strategy at Hankins Aerospace begins with steady growth in our core aerospace parts manufacturing business and extends to increasing our distribution network domestically and abroad. We are expanding our global market presence with targeted acquisitions and a just-in-time manufacturing system that introduces our products to new customers faster than ever before.

The aerospace industry demands higher efficiency and lightweight products to increase fuel economy and reduce environmental impact. With a long history as the leader in aerospace product innovation, Hankins Aerospace continues to anticipate customer needs and thrive in an increasingly competitive pricing environment.

We offer the most innovative manufacturing and advanced technology resources in the aerospace industry. Hankins is known for its market knowledge and extensive technical expertise. Our services range from machining structural parts, engine components, landing gear, and systems controls from super alloys, aluminum, titanium, and stainless steels. We aim to improve manufacturing operations and produce the highest quality parts while increasing productivity and customer satisfaction.

In addition, we are actively diversifying our products, services, and markets. In the past year, we have expanded to offer the following range of aerospace applications.

· Structural

· Fuselage

· Wings

· Tail assembly

· Cockpit

· Landing Gear

· Axle beams

· Main cylinders

· Brakes

· Engine

· Blade

· Casings

· Ducts

· Fittings

· Turbine rings

· Turbo housings

· Interior

· Gallery parts

· Support beams

· Systems Control

· Housings

· Gears

· Hydraulic manifolds

Because Hankins Aerospace is focused on its long-term vision, we strengthen our relationships with suppliers, engineers, contractors, and retailers every day.

Financial Highlights

  Category 2021

2020

Dollar amounts in millions Net sales $895 $804
  Gross profit $173 $144
  Adjusted operating income $42 $37
  Adjusted earnings per share $0.74 $0.71
  Cash and cash equivalents $108 $99
  Total assets $1250 $981
  Total debt $274 $275

Net Sales (Millions) – Past Five Years

2020 $804

2018 $788

2021 $895

2017 $752

2019 $790

2016 $723

Year Sales

Capital Allocation

[insert table here]

Notable Numbers

[insert list here]

Digital Solutions

Hankins Aerospace creates a competitive advantage through custom software solutions that take aerospace manufacturing to the next level of productivity and precision.

Hankins Aerospace, Inc. filings with the SEC, including full financial statements, annual reports from previous years, and this year’s quarterly reports, are available free of charge on our website at hankins.cengage.com.

 

Manage operations on the go

 

 

Hankins SmartSync

 

 

Connect to suppliers

 

 

Hankins Connect

 

 

Analyze data

 

 

Hankins Insight

 

 

This file created specifically for

Capital Structure and leverage

Theme: Capital Structure and leverage

 

Assignment Case 3

Deluxe Corporation

Case 35 page 479

 

GUIDANCE SHEET

 

 

Synopsis

 

In July 2002, an investment banker advising Deluxe Corporation must prepare recommendations for the company’s board of directors regarding the firm’s financial policy. Some special considerations are the mix of debt and equity, maintenance of financial flexibility, and the preservation of an investment-grade bond rating. Complicating the assessment are low growth and technological obsolescence in the firm’s core business.

 

The objective is to recommend an appropriate financial policy for Deluxe Corporation and, in support of that recommendation, it is recommended to show the impact on the cost of capital, financial flexibility (i.e., unused debt capacity), bond rating, and other considerations.

 

Objectives

 

The following are the analytical objectives of this case study:

 

· Survey the determinants of corporate bond ratings. The case highlights the important influence of the rating agencies on the costs of debt and the access to capital markets. The case data afford students the opportunity to explore profitability, coverage ratios, and capitalization ratios as measures of credit quality.

· Explore the practical challenges involved in determining the optimal mix of debt and equity, in particular assessing the tradeoff between the benefits of debt tax shields and the costs of financial distress. The case affords the opportunity to highlight methodological problems in estimating the optimal mix.

· Consider the concepts of debt capacity and financial flexibility. The notion advanced in this case is that flexibility is the ability to access capital without falling short of the firm’s minimum target credit rating.

 

 

 

Questions

 

 

1. What are the risks associated with Deluxe’s business and strategy? What financing requirements do you foresee for the firm in the coming years?

2. What are the main objectives of the financial policy that Rajat Singh must recommend to Deluxe Corporation’s board of directors?

3. Drawing on the financial ratios in case Exhibit 6, how much debt could Deluxe borrow at each rating level? What capitalization ratios would result from the borrowings implied by each rating category?

4. Is Deluxe’s current debt level appropriate? Why or why not?

5. Using Hudson Bancorp’s estimates of the costs of debt and equity in case Exhibit 8, which rating category has the lowest overall cost of funds? Do you agree with Hudson Bancorp’s view that equity investors are indifferent to the increases in financial risk across the investment-grade debt categories?

6. What should Singh recommend regarding:

· the target bond rating

· the level of flexibility or reserves

· the mix of debt and equity

· any other issues you believe should be brought to the attention of the CEO and the board

 

P.S. These questions do require calculations but their accuracy is not critical. It will be enough to provide well explained opinions with supporting analysis.

 

 

Supporting Spreadsheet Files

 

To assist student preparation, a MS Excel File is made available to the students which contains several exhibits and a working forecast model. Students however may develop either their own model if they so desire or use the one provided.

5 Biostatistics Questions

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Biostatistics Team Project 1 ‒ Questions

1. A study is conducted to test a new drug claimed to reduce diastolic blood pressure in adults with a history of coronary heart disease. What is the most efficient study to test whether the drug reduces diastolic blood pressure? Justify your answer.

2. An investigator wants to test whether exposure to secondhand smoke before 1 year of life is associated with development of childhood asthma (defined as asthma diagnosed before 5 years of age). Give two possible study designs and indicate the pros and cons of each. Then, provide your recommendation for the most efficient design.

3. True or False? The following are all examples of observational study designs:

a) Case-control study.

b) Prospective cohort study.

c) Cross-over trial.

d) Retrospective cohort study.

4. A study is run to estimate the incidence of atrial fibrillation (AF) in men and women over the age of 60. Development of atrial fibrillation was monitored over a 10-year follow-up period. The data are summarized below:

 

Developed AF Did not Develop AF
Men 120 6453
Women 86 7074

a) Compute the cumulative incidence of AF in men and in women.

b) Compute the relative risk of AF incidence comparing men to women.

c) Compute the odds ratio of AF incidence comparing men and women.

5. A clinical trial designed to show the efficacy of a new drug in reducing progression to hypertension reports the following:

 

New Drug Placebo
Sample size 200 200
Progression to hypertension 14% 19%

a) Compute the relative risk of progression to hypertension among patients receiving the new drug as compared to the placebo.

b) Compute the difference in proportions of patients progressing to hypertension between the two groups.

c) Compute the odds ratio of progression to hypertension among patients receiving the new drug as compared to the placebo.

6. The following are grade point averages measured in a sample of 8 undergraduate students who are applying to graduate schools in public health.

3.28 2.97 3.05 3.61 3.39 2.95 3.00 3.10

a) Compute the sample mean.

b) Compute the sample standard deviation.

c) Compute the sample median.

7. The following are body mass index (BMI) scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. Body mass index is measured as the ratio of weight in kilograms to height in meters squared.

25 27 31 33 26 28 38 41 24 32 35 40

a) Compute the mean BMI.

b) Compute the standard deviation of BMI.

c) Compute the median BMI.

d) Compute Q1 and Q3.

e) Are there outliers in the distribution of BMI? Justify your answer.

8. A pilot study is run to investigate the effect of a lifestyle intervention designed to increase medication adherence in patients with HIV. Medication adherence is measured as the percentage of prescribed pills that are taken over a one week observation period. Ten patients with HIV agree to participate and their medication adherence before and after the intervention are shown below.

Participant ID Before Intervention After Intervention
1 75% 80%
2 82% 84%
3 66% 70%
4 74% 70%
5 88% 90%
6 66% 75%
7 51% 60%
8 93% 90%
9 88% 90%
10 91% 95%

a) Compute differences in adherence before versus after the intervention for each participant.

b) Compute the mean difference in adherence before versus after the intervention.

c) Compute the standard deviation of the difference in adherence before versus after intervention.

9. True or False? For the standard normal distribution, Q3 = 0.675.

10. A random sample of eight adults, aged 30 years, were asked how much they spent on medical costs in the year 2009. The following data were measured.

300 140 5600 520 470 700 640 1200

a) Compute the sample mean.

b) Compute the sample standard deviation.

c) Compute the sample median.

d) Compute the first and third quartiles.

11. Glucose levels in patients free of diabetes are assumed to follow a normal distribution with a mean of 120 and a standard deviation of 16.

a) What proportion of patients has glucose levels exceeding 115?

b) If a patient has a glucose level of 140, what percentile is this?

c) What is the probability that the mean glucose level exceeds 115 in a sample of 12 patients?

12. The following table shows the numbers of patients classified as underweight, normal weight, overweight, and obese, according to their diabetes status.

 

Underweight Normal Weight Overweight Obese
Diabetes 8 34 65 43
No Diabetes 12 85 93 40

If a patient is selected at random:

a) What is the probability that they are overweight?

b) What is the probability that they are obese and diabetic?

c) What proportion of the diabetics is obese?

d) What proportion of normal-weight patients are not diabetic?

e) What proportion of patients is normal weight or underweight?

13. Approximately 30 percent of obese patients develop diabetes. If a physician sees 10 patients who are obese:

a) What is the probability that half of them will develop diabetes?

b) What is the probability that none will develop diabetes?

c) How many would you expect to develop diabetes?

14. The following table shows the distribution of BMI in children living in U.S. and European urban neighborhoods. (The data are in millions.)

Neighborhood Normal Weight Overweight Obese
US 125 50 40
Europe 101 42 21

Suppose that the probability that a child living in an urban area in the US is obese is 20 percent. A social worker sees 15 children living in urban areas,

a) What is the probability that none are obese?

b) What is the probability that 5 are obese?

15. BMI in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2.

a) A BMI between 25 and 30 is considered overweight. What proportion of children is overweight?

b) A BMI of 30 or more is considered obese. What proportion of children is obese?

c) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?

16. The following data were collected in a survey of 8th graders and summarize their cell phone status.

 

No cell phone Conventional cell phone user Smart phone user
Boys 55 65 35
Girls 31 78 27

a) What proportion of the 8th graders has cell phones?

b) What proportion of the boys does not have cell phones?

c) Is ownership of a cell phone independent of sex? Justify your answer.

d) What proportion of smart phone users are boys?

17. A ferritin test is a popular test to measure a person’s current iron stores. In women, ferritin is approximately normally distributed with a mean of 89 ng/mL and a standard deviation of 23 ng/mL.

a) What is the probability that a woman has a ferritin value of 100 or less?

b) If a woman has a ferritin of 140, what percentile is this?

c) If 50 women are tested, what is the probability that the mean ferritin exceeds 90?

18. With a binomial distribution with n=25 and p=0.48, which is larger:

a) P(12 successes).

b) P(9 successes).

c) P(20 successes).

d) P(10 successes).

19. The following table shows the results of a screening test hypothesized to detect persons at risk for side effects of a new cosmetic surgery.

  Side effects present Side effects absent
Screen positive 12 6
Screen negative 85 204

a) Compute the sensitivity of the test.

b) Compute the specificity of the test.

c) Compute the false positive fraction.

d) Compute the false negative fraction.

20. The following table shows the results of a screening test hypothesized to identify persons at risk for a rare blood disease.

 

No Disease Disease
Screen Negative 1274 28
Screen Positive 51 45

a) Compute the sensitivity of the test.

b) Compute the specificity of the test.

c) Compute the false positive fraction.

d) Compute the false negative fraction.

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