I. Short Answer or True/False (10 pts)
 

(2) 1. Why is the formula for the standard error for the sample proportion in the test statistic different than in the confidence interval?
 

(2) 2. Define the power of the test.
 

True or False (1 pt each).
 

____ 3. The standard error of the mean decreases as the sample size increases. 
 

____ 4. In a one-sided hypothesis test, the p-value is 0.037. This means that the null hypothesis would be rejected at α = 0.05.
 

____ 5. It is not necessary to have equal sample sizes for the paired t test. 
 

____ 6. If the null hypothesis is false, increasing the level of significance, α, for a specified sample size will increase the probability of rejecting the null hypothesis.
 

____ 7. If the calculated value of the t statistic is negative, then there is no evidence that the null hypothesis is false.
 

____ 8. If the null hypothesis is rejected for a two-tailed test, then it will also be rejected for a one-tailed hypothesis test.
 

II. Problems (90 points). SHOW ALL CALCULATIONS!!

1. Each year, J.D. Powers and Associates compiles the Customer Satisfaction Index for the automobile industry. In 2003, in addition to many other measures, a satisfaction index was found for a simple random sample of 10 passenger cars including: Acura, Chevrolet, Ford, Mercedes, Toyota, Volvo, and others. Satisfaction scores ranged from 117 to 144 and partial results are:

Σx = 1258 s² =94.62

The researcher wishes to calculate a 99% confidence interval for the population mean satisfaction index based on the 2003 sample.
 

(4) a) What assumptions must be made for the confidence interval to be valid?
 

(8) b) Construct the 99% confidence interval. 
 

(4) c) Write a sentence interpreting the interval.
 

(4) d) Using the confidence interval found for 2003, is it likely that the average satisfaction has increased from 2002 when it was 119 for all passenger cars? Explain.
 

2. Americans shop for food, clothing, housewares, furniture, and other necessities and luxuries week after week. But is shopping considered a pleasant or unpleasant experience? A researcher surveyed 129 women and 68 men to determine each respondent’s opinion on the pleasantness of shopping. Test to see if women and men differ in their opinions on shopping. Use the SPSS printout attached. Let α = .01.
 

(4) b) State the hypotheses in words and symbols (steps 1 and 2).
 

(8) c) Give the test statistic value and give reasons for its use (step 3).
 

(4) d) Find the p-value, (step 4, no statement for this problem).
 

(4) e) State the decision in symbols and in words (steps 5 and 6).
 

3. A college chemistry instructor is concerned about the detrimental effect of poor mathematics background on his students. He randomly selects 15 students and divides them according to math background. Their semester grade averages are the following:
 
 

Less than 2 yrs of HS algebra 58 61 81 64 74 43

2 or more years of HS algebra84 92 75 67 83 81 65 52 74
 

Results are given on the attached SPSS printout. Let α = .05. 
 

Is there enough evidence to show that students with less than 2 years of HS algebra performed poorer in chemistry than those with more algebra?
 

(4) a) State the hypotheses in words and symbols (steps 1 and 2).
 

(5) b) What assumptions must be made in order for the test results to be valid?

       Do they hold? Explain using the SPSS results.
 

(4) c) Give the test statistic value (step 3).
 

(8) d) Find the p-value and write a statement interpreting it in this problem,(step 4).
 

(4) e) State the decision in symbols and in words (steps 5 and 6).
 

4. Potential advertisers value television's well-known Nielsen ratings as a barometer of a TV show's popularity among viewers. The Nielsen rating of a certain TV program is an estimate of the proportion of viewers, expressed as a percentage, who tune their sets to the program on a given night. Suppose the Nielsen ratings are to be found for a premiere of a new hospital drama show using a simple random sample. 
 

(7) a) If no information is known about the possible rating, what sample size should the researcher use for a 90% confidence interval in order to obtain a margin of error of 6%.
 

(3) b) The researcher takes a sample of the size you found above and finds that 119 families watched the premiere. In order to perform the confidence interval calculations, what assumptions must be made? Do they hold? Explain.
 

(8) c) Calculate the 90% confidence interval using the 119 families from your sample size. 
 

(4) d) Write a confidence interval statement.
 

(3) e) Did the confidence interval meet the requirement on the margin of error? Explain.