# Statistics- Which distribution should you use for this problem

Question

1.You were interested in how long the average psychology major at your college

studies per night, so you asked 10 psychology majors to tell you the amount they

study. They told you the following times: 2, 1.5, 3, 2, 3.5, 1, 0.5, 3, 2, 4.

(a) Find the 95% confidence interval on the population mean.

(b) Find the 90% confidence interval on the population mean.

2. In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a

standard deviation of $3,156. Assume the underlying distribution is approximately

normal.

a. Which distribution should you use for this problem? Explain your choice.

b. Define the random variable X ¯ in words.

c. Construct a 95% confidence interval for the population mean cost of a used car.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

d. Explain what a “95% confidence interval” means for this study.

3. A quality control specialist for a restaurant chain takes a random sample of size

12 to check the amount of soda served in the 16 oz. serving size. The sample mean

is 13.30 with a sample standard deviation of 1.55. Assume the underlying

population is normally distributed.

What is the error bound?

a. 0.87

b. 1.98

c. 0.99

d. 1.74

4. An article regarding interracial dating and marriage recently appeared in the

Washington Post. Of the 1,709 randomly selected adults, 315 identified themselves

as Latinos, 323 identified themselves as blacks, 254 identified themselves as

Asians, and 779 identified themselves as whites. In this survey, 86% of blacks said

that they would welcome a white person into their families. Among Asians, 77%

would welcome a white person into their families, 71% would welcome a Latino,

and 66% would welcome a black person.

a. We are interested in finding the 95% confidence interval for the percent of all

black adults who would welcome awhite person into their families. Define the

random variables X and P′, in words.

b. Which distribution should you use for this problem? Explain your choice.

c. Construct a 95% confidence interval.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

5.You choose an alpha level of .01 and then analyze your data.

a. What is the probability that you will make a Type I error given that the null

hypothesis is true?

b. What is the probability that you will make a Type I error given that the null

hypothesis is false?

6. Below are data showing the results of six subjects on a memory test. The three

scores per subject are their scores on three trials (a, b, and c) of a memory task. Are

the subjects getting better each trial? Test the linear effect of trial for the data.

abc

467

378

285

147

469

242

a. Compute L for each subject using the contrast weights -1, 0, and 1. That is,

compute (-1)(a) + (0)(b) + (1)(c) for each subject.

b. Compute a one-sample t-test on this column (with the L values for each subject)

you created.

7. You are conducting a study to see if students do better when they study all at

once or in intervals. One group of 12 participants took a test after studying for one

hour continuously. The other group of 12 participants took a test after studying for

three twenty minute sessions. The first group had a mean score of 75 and a

variance of 120. The second group had a mean score of 86 and a variance of 100.

a. What is the calculated t value? Are the mean test scores of these two groups

significantly different at the .05 level?

b. What would the t value be if there were only 6 participants in each group?

Would the scores be significant at the .05 level?

8. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different

people. Of interest is whether the liquid diet yields a higher mean weight loss than

the powder diet. The powder diet group had a mean weight loss of 42 pounds

with a standard deviation of 12 pounds. The liquid diet group had a mean weight

loss of 45 pounds with a standard deviation of 14 pounds.

9. A golf instructor is interested in determining if her new technique for improving

players’ golf scores is effective. She takes four new students. She records their 18hole scores before learning the technique and then after having taken her class.

She conducts a hypothesis test. The data are as follows.

Player 1

Player 2

Player 3

Player 4

Mean score 83

78

93

87

before class

Mean score 80

80

96

86

after class

The correct decision is:

a. Reject H0.

b. Do not reject the H0.

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