This practice exam consists of 25 multiple choice questions and is similar (in format, types of questions, etc.) to the exam you will take for credit. The time limit for all module exams is 2 hours. It is recommended that you take this practice exam under exam conditions in order to prepare for the module exam. When you are finished with the exam you can check your answers by clicking here.  The module exams are worth 100 points (4 points per question).
 

The next two questions refer to the following situation. The quality control manager at a particular soft drink
company wants to estimate the actual amount of soft drink placed in 12 ounce cans. Past experience has
indicated that the process standard deviation is 0.78 ounces. A random sample of 50 twelve ounce cans
produced a sample average of 11.8 ounces.

1.) What is a 95% interval estimate for the true average amount of soft drink in each can?

a. (11.584, 12.016)
b. (11.776, 11.824)
c. (10.271, 13.329)
d. (11.690, 11.910)
e. (11.619, 11.981)

2.) Suppose they took a random sample of 100 twelve ounce cans and a 95% interval estimate was obtained.  Which one of the following statements is correct?

a. The interval width with n=100 will be larger than the interval width with n=50.
b. There will be no change between the two intervals.
c. The interval widths will be identical.
d. The interval width with n=100 will be smaller than the interval width with n=50.
e. The lower and upper endpoints of the two intervals will be identical.
 

The next two questions refer to the following situation. History shows that 50% of NDSU students change their
major area of study after their first year in the program. A simple random sample of 100 NDSU students
revealed that 52 had changed their major area of study after their first year of the program. Using an a = 0.01
level of significance, test if there has been a significant increase in the proportion of NDSU students who
change their major after the first year in the program.

3.) What is the value of the test statistic for this situation?

a. 0.50
b. 2.57
c. 0.52
d. 2.33
e. 0.40

4.) Which one of the following statements is the correct conclusion for the test?

a. Reject H₀ since z > 0.52
b. Fail to reject H₀ since z < 2.33
c. Reject H₀ since z > 2.33
d. Fail to reject H₀ since z > 0.01
e. Reject H₀ since z < 2.33
 

The next question refers to the following situation. A random sample of a company's monthly operating
expenses for 36 months produced a sample mean of $5470 per month and a standard deviation of $760 per
month.

5.) What is a 95% interval estimate for the company's mean monthly expenses?

a. (5255.98, 5684.02)
b. (3905.84, 7034.16)
c. (3950.00, 6990.00)
d. (5427.14, 5512.86)
e. (5212.85, 5727.15)
 

The next two questions refer to the following situation. A random sample of 23 financial institutions in California was selected and the interest rate charged for credit cards was recorded for each. An investigator wants to know if the variation (i.e. variance) in interest rates is larger than 4.0%. The data was input into Data Desk and Data Desk produced the following output. You can assume an a = 0.01 level of significance.

Chi-square Test for Variances
Individual Alpha Level 0.01

Rates: Test Ho: Variance(Rates) = 4 vs Ha: Variance(Rates) > 4
Sample Variance = 5.4196017 Chi-square Test for Variances Statistic = ???? w/22 df
p = 0.1232

6.) What is the value of the test statistic for this situation?

a. 5.42
b. 59.62
c. 29.81
d. 161.57
e. 40.29

7.) Which of the following statements is the correct conclusion for the test?

a. The variation in interest rates for credit cards in California is larger than 4.0% since the test statistic > 40.29
b. The variation in interest rates for credit cards in California is larger than 4.0% since p-value > 0.01
c. The variation in interest rates for credit cards in California is not larger than 4.0% since the test statistic > 5.42
d. The variation in interest rates for credit cards in California is not larger than 4.0% since p-value > 0.01
e. The variation in interest rates for credit cards in California is larger than 4.0% since the test statistic > 0.01
 

The next question refers to the following situation. A random sample of 100 wholesalers who buy plastic pipe
indicated that 59 plan to increase their purchases in the coming year.

8.) What is a 99% interval estimate for the true proportion of wholesalers who plan to increase their
purchases in the upcoming year?

a. (0.463, 0.717)
b. (0.577, 0.603)
c. (0.584, 0.596)
d. (0.475, 0.705)
e. (0.494, 0.686)
 

The next two questions refer to the following situation. A marketing research group reports that the typical
supermarket shopper uses an average of $1.40 in coupons per week. It is known that the standard deviation for
amount used in coupons is $0.62. A random sample of 50 shoppers revealed an average of $1.54 used in
coupons. Wishing to refute the report's claim, an a = 0.10 level of significance test was conducted. A test
statistic value of 1.59 was produced.

9.) What are the appropriate hypotheses for testing this situation?

a. H₀: m = 1.54 vs. H_a: m < 1.54
b. H₀: m = 1.40 vs. H_a: m < 1.40
c. H₀: m = 1.40 vs. H_a: m > 1.40
d. H₀: m = 1.40 vs. H_a: m 1.40
e. H₀: m = 1.54 vs. H_a: m 1.54

10.) What are the p-value and conclusion for this test, respectively?

a. 0.8882, Fail to Reject H₀
b. 0.0559, Fail to Reject H₀
c. 0.1118, Reject H₀
d. 0.1118, Fail to Reject H₀
e. 0.0559, Reject H₀
 

The next two questions refer to the following situation. A simple random sample of 15 residents from
Fargo was selected and the number of miles traveled in their automobile per day was recorded for each.
The sample mean was 20.2 and the sample standard deviation was 6.2.

11.) What is a 90% interval estimate for the mean number of miles residents of Fargo travel per day in an
automobile?

a. (18.05, 22.35)
b. (17.38, 23.02)
c. (15.98, 24.42)
d. (19.47, 20.93)
e. (10.01, 30.39)

12.) Assuming the population standard deviation is 6.2, what sample size is necessary to estimate the true
mean number of miles to within 1 mile with 99% accuracy?

a. 209
b. 99
c. 15
d. 255
e. 16
 

The next question refers to the following situation.  In the American legal system, a defendant is presumed innocent until proven guilty. Consider then a null hypothesis H₀ that the defendant is innocent and an alternative hypothesis H_a that the defendant is guilty.

13.) Assuming the jury found the defendant guilty when he was really innocent, what type of error was made?

a.) Critical error
b.) b error
c.) Type II error
d.) Type III error
e.) Type I error
 

The next question refers to the following situation. A university professor randomly selected 150 students and
found that 45 of the students "skipped" at least one class per week.

14.) What is a 95% interval estimate for the true proportion of students that "skip" at least one class per week?

a. (0.297, 0.303)
b. (0.238, 0.362)
c. (0.227, 0.373)
d. (0.263, 0.337)
e. (0.212, 0.388)
 

The next two questions refer to the following situation. The Television Advertising Institute claims that, on the
average, adults spend 2.9 hours or more watching television on Thursday nights during the prime time hours of
6:00 to 12:00. In an effort to verify this claim, a random sample of 36 adults was taken and a sample mean of
2.4 hours was obtained. Also, past studies have shown that the population standard deviation is 0.6 hour. Using
a significance level of a = 0.01, is there evidence that suggests the Institute's claim is false?

15.) What is the appropriate test statistic value for this test?

a. -5.00
b. -0.83
c. -2.33
d. -2.40
e. -2.57

16.) Which one of the following statements is the correct rejection region for the test?

a. Reject H₀ if t > 2.43
b. Reject H₀ if z > 1.96
c. Reject H₀ if z < -2.57
d. Reject H₀ if z < -2.33
e. Reject H₀ if t < -0.83
 

The next question refers to the following situation. A television documentary on overeating claimed that
Americans are about 10 pounds overweight on average. Eighteen randomly selected individuals
were examined, and their average excess weight was found to be 12.4 pounds with a sample standard
deviation of 2.7 pounds.

17.) What is a 90% interval estimate for the true population standard deviation?

a. (2.120, 3.780)
b. (2.181, 3.890)
c. (5.889, 10.503)
d. (5.723, 10.207)
e. (2.072, 3.633)
 

The next two questions refer to the following situation. A check cashing service has found that approximately
5% of all checks submitted to the service for cashing are "bad". After instituting a check verification system
the service collected data and calculated a test statistic value of 1.34. Suppose we wish to test if the proportion
of "bad" checks currently being cashed has changed from 5% using an a = 0.10 level of significance.

18.) What are the appropriate hypotheses for this situation?

a. H₀: p = 0.05 vs. H_a: p 0.05
b. H₀: m = 0.10 vs. H_a: m 0.10
c. H₀: m = 0.05 vs. H_a: m > 0.05
d. H₀: p = 0.10 vs. H_a: p < 0.10
e. H₀: p = 0.05 vs. H_a: p < 0.05

19.) Which one of the following statements about the conclusion of the test is correct?

a. Fail to Reject H₀ since p-value < 0.05
b. Fail to Reject H₀ since p-value > 0.10
c. Reject H₀ since p-value < 0.10
d. Reject H₀ since p-value > 0.10
e. Reject H₀ since p-value < 0.05
 

The next two questions refer to the following situation.  Forty fields are selected from a population of several thousand fields for an agriculture experiment. The 40 fields are planted with a new variety of corn and at harvest time the yield is determined for each field. The average yield for these fields is  = 130 bushels per acre. Assume that s = 10.

20.) Find a 90% confidence interval for the mean yield m for this variety of corn.

a. (127.98 , 132.02)
b. (127.94 , 132.06)
c. (127.34 , 132.66)
d. (127.40 , 132.60)
e. (126.90 , 133.10)

21.) Interpret the above interval:

a. There is a 90% probability that the true average yield is in the interval.
b. We are 90% confident that the next harvest yield will be in the interval.
c. 90% of all intervals will include  = 130.
d. We are 90% confident that the population average yield is in the interval.
e. 90% of the time,  = 130 will be in the interval.
 

The next two questions refer to the following situation. A simple random sample of 22 observations from a
given population produced a sample mean of 13 and a sample standard deviation of 8. Suppose we wish to test
if the population mean is less than 15 at an a = 0.10 level of significance.

22.) Which one of the following statements about the test statistic is correct?

a. z = 3.32
b. t = -1.17
c. t = -0.25
d. t = -5.50
e. z = 2.00

23.) Which one of the following statements is the correct rejection region for the test?

a. Reject H₀ if z > 1.6450
b. Reject H₀ if t < -1.3232
c. Reject H₀ if t < -1.3212
d. Reject H₀ if t < -1.7207
e. Reject H₀ if z > 1.2800
 

The next question refers to the following situation.  A simple random sample of 30 items produced a sample mean of 25.272 and a sample standard deviation of 4.167. Suppose 80%, 90%, 92%, 95%, and 99% confidence intervals were calculated from this data.

24.) Which of the following intervals represents the 99% confidence interval for the true mean of the population?

a. (24.27, 26.27)
b. (23.89, 26.65)
c. (23.17, 27.37)
d. (23.98, 26.57)
e. (23.72, 26.83)
 

The next question refers to the following situation. Suppose we wish to test the hypotheses H₀: m = 20 vs. H_a: m > 20 using a t-test and significance level of a = 0.10. A test statistic value of 2.08 was calculated from a random sample of size 21.

25.) What are the bounds on the true p-value for this test?

a. 0.010 < p-value < 0.025
b. 0.050 < p-value < 0.100
c. 0.100 < p-value < 0.250
d. 0.005 < p-value < 0.010
e. 0.025 < p-value < 0.050
 

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