Show work/explanation where indicated. Answers without any work may earn little, if any,
credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document
containing your work. Scanned work is acceptable also. In your document, be sure to include your
name and the assertion of independence of work. 1. Suppose that an accounting firm does a study to determine the time needed to
complete one person’s tax forms. It randomly surveys 100 people. The sample mean
is 23.6 hours. There is a known population standard deviation of 7.0 hours. The
population is assumed to be normal.
a. Find the following:
i. ´x =¿ ii. σ =¿ iii. n=¿
X´ =¿ b. In words, c. Which distribution should you use for this problem?
d. Construct a 90% confidence interval for the population mean time to complete the
tax forms.
2. The grade point averages (GPA) for 10 randomly selected college freshmen are listed
below. Assume the grade point averages are normally distributed.
2.
0 3.
2 1.
8 2.
9 0.
9 4.
0 3.
3 2.
9 3.
6 0.
8 a. Find the following:
i. ´x =¿ ii. s x =¿ iii. n=¿ iv. n−1=¿ b. Which distribution should you use for this problem? c. Construct a 95% confidence interval for the population mean GPA of college
freshmen.
d. What will happen to the (a) error bound and (b) confidence interval if 500 college
freshmen are selected? 3. (Select the correct answer) When a 99% confidence interval is calculated instead of
a 95% confidence interval with n being the same, the maximum error of estimate will
be
a. Smaller
b. Larger
c. The same
d. It cannot be determined 4. (Select the correct answer) A survey of 280 homeless persons showed that 63 were
veterans. Construct a 90% confidence interval for the proportion of homeless persons
who are veterans.
a. ( 0.161, 0.289 ) b. ( 0.167, 0.283 ) c. ( 0.184, 0.266 ) d. ( 0.176, 0.274 ) 5. (Select the correct answer) Suppose you are using α =0.01 to test the claim that
μ ≤32 using a P-value. You are given the sample statistics n=40 , ´x =33.8 , and σ =4.3 . Find the P-value.
a. 0.0040
b. 0.1030
c. 0.0211
d. 0.9960 6. (Select the correct answer) Suppose you want to test the claim that μ1 > μ2 . Two samples are randomly selected from each population. If a hypothesis test is
performed, how should you interpret a decision that rejects the null hypothesis?
μ1 > μ2 a. There is sufficient evidence to support the claim b. There is not sufficient evidence to support the claim
c. There is not sufficient evidence to reject the claim
d. There is sufficient evidence to reject the claim μ1 > μ2
μ1 > μ2 μ1 > μ2 7. The mean number of sick days an employee takes per year is believed to be about ten.
Members of a personnel department do not believe this figure. They randomly survey
eight employees. The number of sick days they took for the past year are as follows:
12; 4; 15; 3; 11; 8; 6; 8. Let x = the number of sick days they took for the past year.
Should the personnel team believe that the mean number is ten? Use α=0.05 . a. State H0 and Ha b. Identify the random variable (sample statistic) c. State the distribution for the test d. Calculate the P-value e. Graph the distribution f. Interpret the P-value and compare to α g. Make a decision regarding H0 h. State the conclusion 8. The National Institute of Mental Health published an article stating that in any oneyear period, approximately 9.5 percent of American adults suffer from depression or a
depressive illness. Suppose that in a survey of 100 people in a certain town, seven of
them suffered from depression or a depressive illness. Conduct a hypothesis test to
determine if the true proportion of people in that town suffering from depression or a
depressive illness is lower than the percent in the general adult American population.
a. State H0 and Ha b. Identify the random variable (sample statistic) c. State the distribution for the test d. Calculate the P-value e. Graph the distribution f. Interpret the P-value and compare to α g. Make a decision regarding H0 h. State the conclusion 9. A dietician wishes to see if a person’s cholesterol level will change if the diet is
supplemented by a certain mineral. Six subjects were pretested and then took the
mineral supplement for a six-week period. The results are shown in the table. Can it
be concluded that the cholesterol level has been changed at a significance level of
10%? Assume the variable is approximately normally distributed.
Subject
Before
( X1) A
21
0 B
23
5 C
20
8 D
19
0 E
17
2 F
24
4 After 19 17 21 18 17 22 0 ( X2) a. State H0 and 0 0 8 3 8 Ha b. Identify the random variable (sample statistic) c. State the distribution for the test d. Calculate the P-value e. Graph the distribution f. Interpret the P-value and compare to α g. Make a decision regarding H0 h. State the conclusion 10. According to a recent survey of 1,200 people, 61% feel that the president is doing an
acceptable job. We are interested in the population proportion of people who feel the
president is doing an acceptable job.
a. Define the random variables X and P ' in words. b. Which distribution should you use for this problem? Explain your choice. c. Construct a 90% confidence interval for the population proportion of people who
feel the president is doing an acceptable job.
i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound.

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