SDS 302 - Homework 4 complete solutions correct answers key

SDS 302 - Homework 4 complete solutions correct answers key

Excel (6 pts)

You will use the dataset from the one-sample t-test pre-lab to answer the following question. Run the appropriate analysis in Excel and then write a short paragraph to answer the question.  The paragraph should include:
1.  The null and alternative hypothesis
2.  The results of your Excel analysis including t-statistic, critical value, and p-value
3.  Conclusion including an interpretation of these results and a final answer to the question

Waist-hip ratios (WHR), or a person’s waist size divided by their hip size, is replacing BMI as an index of obesity and risk of cardiovascular disease. WHR over 0.85 are considered to be unhealthy and at risk for cardiovascular issues. Re-evaluate the hypothesis in the One-Sample T-test Lab (many people are overweight when they are diagnosed with type 2 diabetes) to investigate if the group of diabetics has an average WHR higher than 0.85. (Note: first you will have to calculate the WHR for each diabetic patient.)

Problems (24 points)

1.      The following results were obtained from Excel on a difference test for the IQ scores of oldest children of a family and only children. Researchers randomly selected children from the population in order to test if the IQ scores for the only children were higher than oldest children. (7 pts)

Only

Oldest

Mean

118.25

114.67

Variance

392.39

178.79

Observations

110

101

Hypothesized Mean Difference

0

a.       Write the null and alternative hypothesis for this test.

b.      Are the assumptions necessary for inference met?

c.       Perform the appropriate test including the formula that you used, the calculated value of the t-statistic (show all work!), and the t-critical you compared to your t-statistic.

d.      State your conclusion.

2.      The aluminum bottle, has become popular with beverage manufactures. Besides being lightweight and requiring less packaging, the aluminum bottle is reported to cool faster and stay cold longer than typical glass bottles. A small brewery tests this claim and obtains the following information regarding the time (in minutes) required to chill a bottle of beer from room temperatures (75ºF) to serving temperature (45ºF). 45 clear glass bottles were tested with a mean time to chill of 133.8 minutes (s = 9.9) and 35 aluminum bottles were tested with a mean time to chill of 92.4 minutes (s = 7.3). (8 pts)

a.       What is the 80% confidence interval for the mean difference in cooling time for clear glass versus aluminum?

b.      What is the 95% confidence interval for the mean difference in cooling time for clear glass versus aluminum?

c.       What does the 95% confidence interval indicate about the differences in cooling time?

3.      The following data represent the daily rental for a compact automobile charged by two car rental companies in 9 locations. You want to test whether Thrifty has a significantly different cost than Hertz on average. Conduct a paired samples t-test to test the difference in prices across the list of cities. (9 pts)

City

Thrifty

Hertz

Chicago

21.81

18.99

Los Angeles

29.89

48.99

Houston

17.90

19.99

Orlando

27.98

35.99

Boston

24.61

25.60

Seattle

21.96

22.99

Pittsburgh

20.90

19.99

Phoenix

47.74

36.99

New Orleans

33.81

26.99

a.       What are the null and the alternative hypotheses?

b.      Are the assumptions necessary for inference met?

c.       Perform the appropriate test including the formula that you used, the calculated value of the t-statistic (show all work!), and the t-critical you compared to your t-statistic.

d.      State your conclusion.