Statistics homework 9 questions complete solutions correct answers key

Statistics homework 9 questions complete solutions correct answers key

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.

a b c

4 6 7

3 7 8

2 8 5

1 4 7

4 6 9

2 4 2

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 18-hole 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 before class

83

78

93

87

Mean score after class

80

80

96

86

The correct decision is:

a. Reject H0.

b. Do not reject the H0.