Statistics homework help. STAT 3300 Homework #2

Due Monday, 05/18/2020

Note: Answer these questions on a separate piece of paper. In the top right corner, include

your name, SMU ID, and course number. Please include a title for the assignment so that

it is clear to the graders. If you miss class the day the assignment is turned in, submit this

before class in order to receive credit.

Question 1 (20 points total)

Researchers were interested in comparing the long-term psychological effects of being on a high-carbohydrate,

low-fat (LF) diet versus a high-fat, low-carbohydrate (LC) diet. A total of 106 overweight and obese

participants were randomly assigned to one of these two energy-restricted diets. At 52 weeks, 32 LC dieters

and 33 LF dieters remained. Mood was assessed using a total mood disturbance score (TMDS), where a

lower score is associated with a less negative mood. A summary of these results follows:

Group n x¯ s

LC 32 47.3 28.3

LF 33 19.3 25.8

Is there a difference in the TMDS at Week 52? Test the null hypothesis that the dieters’ average mood in the

two groups is the same. Use a significance level of 0.05.

Question 2 (20 points total)

In the previous question, the data was analyzed using the two-sample t test that does not assume equal

standard deviations. Repeat the analysis, but conduct a pooled two-sample t test that does assume equal

standard deviations.

Question 3 (15 points total, 5 points each)

You are designing a study to test the null hypothesis that µ = 0 versus the alternative that µ is positive.

Assume that σ is 20. Suppose that it would be important to be able to detect the alternative µ = 4. Use

α = 0.05.

a) What sample size is needed to detect this alternative with power of at least 0.80?

b) What sample size is needed to detect this alternative with power of at least 0.90?

c) With sample size at 200, what is the power of the test?

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Question 4 (15 points total, 5 points each)

In exercise 79 (p.53) of the text, the diameter at breast height (DBH) data for longleaf pine trees in two parts

of the Wade Tract are compared. Suppose that you are planning a similar study in which you will measure the

diameters of longleaf pine trees. Based on exercise 79, you are willing to assume that the standard deviation

for both halves is 20 cm. Suppose that a difference in mean DBH of 10 cm or more would be important to

detect. You will use a t statistic and a two-sided alternative for the comparison.

a) Find the power if you randomly sample 20 trees from each area to be compared.

b) Repeat the calculations for 60 trees in each sample.

c) If you had to choose between the 20 and 60 trees per sample, which would you choose? Give reasons

for your answer.

Question 5 (14 points total)

Consider the following data set. The data were actually collected in pairs, and each row represents a pair.

Group 1 Group 2

48.86 48.88

50.60 52.63

51.02 52.55

47.99 50.94

54.20 53.02

50.66 50.66

45.91 47.78

48.79 48.44

47.76 48.92

51.13 51.63

Note: the data are stored in the file ‘PAIRED.csv’.

a) (6 points) Suppose that we ignore the fact that the data were collected in pairs and mistakenly treat this

as a two-sample problem. Compute the sample mean and variance for each group. Then compute

the two-sample t statistic, degrees of freedom, and p-value for the two-sided alternative.

b) (6 points) Now analyze the data in the proper way. Compute the sample mean and variance of the

differences. Then compute the t statistic, degrees of freedom, and p-value for the two-sided alternative.

c) (2 points) Describe the differences in the two test results.

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Question 6 (16 points total, 8 for the entree data and 8 for the wine data)

In one study, 39 diners were given a free glass of cabernet sauvignon wine to accompany a French meal.

Although the wine was identical, half the bottle labels claimed the wine was from California and the other half

claimed it was from North Dakota. The following table summarizes the grams of entree and wine consumed

during the meal.

Did the patrons who thought that the wine was from California consume more food and beverage? Analyze

the data and write a report summarizing your work. Be sure to include details regarding the statistical

methods you used, your assumptions, and your conclusions. You will need to carry out two separate analyses:

one for the entrees, and one for the wine.

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