# Statistics- Which distribution should you use for this problem

March 31, 2017

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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