stats (NEED IN 4 HOURS)

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1. For each of the following situations give the degrees of freedom and an appropriate bound on the P-value (give the exact value if you have software available) for the χ2 statistic for testing the null hypothesis of no association between the row and column variables.

(a) A 2 by 2 table with χ2 = 0.94.

df =
P-value =

(b) A 4 by 4 table with χ2 = 18.96.

df =
P-value =

df =
P-value =

(d) A 5 by 3 table with χ2 = 13.02.

df =
P-value =

2. A recent study of undergraduates looked at gender differences in dieting trends. There were 187 women and 107 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:

	Gender
Tried low-fat diet	Women	Men
Yes	38	9
No

(a) Fill in the missing cells of the table.

	Gender
Tried low-fat diet	Women	Men
Yes	38	9
No

(b) Summarize the data numerically. What percent of each gender has tried low-fat diets? (Round your answers to two decimal places.)

women	%
men	%

(c) Test that there is no association between gender and the likelihood of trying a low-fat diet. (Round your χ2 to three decimal places, and round your P-value to four decimal places.)

χ2	=
df	=
P-value	=

Summarize the results.

There is strong evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.

There is no evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.

3. In what ways do advertisers in magazines use sexual imagery to appeal to youth? One study classified each of 1500 full-page or larger ads as "not sexual" or "sexual," according to the amount and style of the dress of the male or female model in the ad. The ads were also classified according to the age group of the intended readership. Here is a summary of the data.


	Magazine readership age group

Model dress	Young adult	Mature adult

Not sexual (percent)	72.8%	75.6%
Sexual (percent)	27.2%	24.4%

Number of ads	1000	500

Perform the significance test that compares the model dress for the age groups of magazine readership. Summarize the results of your test. (Use α = 0.05. Round your χ2 to three decimal places and round your P-value to four decimal places.)

χ2	=
P-value	=

Give your conclusion.

Reject the null hypothesis. There is not significant evidence of an association between model dress and age group.Reject the null hypothesis. There is significant evidence of an association between model dress and age group. Fail to reject the null hypothesis. There is not significant evidence of an association between model dress and age group.Fail to reject the null hypothesis. There is significant evidence of an association between model dress and age group.

4. A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 65 college students were compared with the behaviors of 55 nonstudents. One of the questions was "When asked to create a password, I have used either my mother's maiden name, or my pet's name, or my birth date, or the last four digits of my social security number, or a series of consecutive numbers." For the students, 23 agreed with this statement while 28 of the nonstudents agreed.

(a) Display the data in a two-way table.

	Students	Nonstudents	Total
Agreed
Disagreed
Total			120

Perform the chi-square test. (Round your χ2 to three decimal places and round your P-value to four decimal places.)

χ2	=
df	=
P-value	=

Summarize the results.

We cannot conclude at the 5% level that students and nonstudents differ in the response to this question.We can conclude at the 5% level that students and nonstudents differ in the response to this question.

(b) Reanalyze the data using the methods for comparing two proportions that we studied in the previous chapter. Compare the results and verify that the chi-square statistic is the square of the z statistic. (Test students who agreed minus nonstudents who agreed. Round your z to two decimal places and round your P-value to four decimal places.)

z	=
P-value	=

(c) The students in this study were junior and senior college students from two sections of a course in Internet marketing at a large northeastern university. The nonstudents were a group of individuals who were recruited to attend commercial focus groups on the West Coast conducted by a lifestyle marketing organization. Discuss how the method of selecting the subjects in this study relates to the conclusions that can be drawn from it.

5. Suppose that there is a linear relationship between the number of students x in a school system and the annual budget y. Write a population regression model to describe this relationship.

yi = β0 + β1xi + εi

yi = β0 + β1xi + β2xi + εi

= b0 + b1xi

= b0 + b1xi + εi

yi = β0 + β1xi

(a) Which parameter in your model is the fixed cost in the budget (for example, the salary of the principals and some administrative costs) that does not change as xincreases?

b1β1 b0εi β0

(b) Which parameter in your model shows how total cost changes when there are more students in the system?

εi β1 b0b1β0

Do you expect this number to be greater than 0 or less than 0?

greater than 0less than 0

(c) Actual data from various school systems will not fit a straight line exactly. What term in your model allows variation among schools of the same size x?

εi β0 b0β1 b1

6. The SAT and the ACT are the two major standardized tests that colleges use to evaluate candidates. Most students take just one of these tests. However, some students take both. The data data386.dat gives the scores of 60 students who did this. How can we relate the two tests?

(a) Plot the data with SAT on the x axis and ACT on the y axis. Describe the overall pattern and any unusual observations. (b) Find the least-squares regression line and draw it on your plot. Give the results of the significance test for the slope. (Round your regression slope and intercept to three decimal places, your test statistic to two decimal places, and your P-value to four decimal places.)

ACT =	+ (SAT)
t =
P =

7. Returns on common stocks in the United States and overseas appear to be growing more closely correlated as economies become more interdependent. Suppose that the following population regression line connects the total annual returns (in percent) on two indexes of stock prices:

MEAN OVERSEAS RETURN = 4.9 + 0.68 × U.S. RETURN

(a) What is β0 in this line?

β0 is the population slope, 0.68.β0 is the population intercept, 0.68. β0 is the population slope, 4.9.β0 is the population intercept, 4.9.

What does this number say about overseas returns when the U.S. market is flat (0% return)?

This says that the mean overseas return is % when the U.S. return is 0%.

(b) What is β1 in this line?

β1 is the population slope, 0.68.β1 is the population intercept, 4.9. β1 is the population intercept, 0.68.β1 is the population slope, 4.9.

What does this number say about the relationship between U.S. and overseas returns?

This says that when the U.S. return changes by 1%, the mean overseas return changes by %.

(c) We know that overseas returns will vary in years having the same return on U.S. common stocks. Write the regression model based on the population regression line given above.

yi = + xi + εi,

where yi and xi are observed overseas and U.S. returns in a given year, and εi are independent N(0, σ) variables.

What part of this model allows overseas returns to vary when U.S. returns remain the same?

σi εi

8. How are returns on common stocks in overseas markets related to returns in U.S. markets? Measure U.S. returns by the annual rate of return on the Standard & Poor's 500-Stock Index and overseas returns by the annual rate of return on the Morgan Stanley EAFE (Europe, Australasia, Far East) index. Both are recorded in percents. Regress the EAFE returns on the S&P 500 returns for the 24 years 1976 to 2000. Here is part of the output for this regression. The regression equation is EAFE = 5.14 + 0.618 S&P. (Round your answer for F to two decimal places and your answers for SS and MS to one decimal place.) for

Analysis of Variance
Source	DF	SS	MS	F
Regression	1	1491.4	1491.4
Residual Error
Total	23	13565.3

Complete the analysis of variance table by filling in the missing boxes. (Round your answer for s to two decimal places and your answer for r2 to three decimal places.) What is s? What is r2?

9. We assume that our wages will increase as we gain experience and become more valuable to our employers. Wages also increase because of inflation. By examining a sample of employees at a given point in time, we can look at part of the picture. How does length of service (LOS) relate to wages? The data here (data184.dat) is the LOS in months and wages for 60 women who work in Indiana banks. Wages are yearly total income divided by the number of weeks worked. We have multiplied wages by a constant for reasons of confidentiality.

(a) Plot wages versus LOS. Consider the relationship and whether or not linear regression might be appropriate. (Do this on paper. Your instructor may ask you to turn in this graph.) (b) Find the least-squares line. Summarize the significance test for the slope. What do you conclude?

Wages =	+ LOS
t =
P =

This answer has not been graded yet.

(d) Give a 95% confidence interval for the slope. ( , )