1. A paint manufacturer claims its paint will last an average of 16 years. Assume that paint life is normally distributed with a standard deviation of 3.2 years. Suppose a random sample of 20 houses are painted with this manufacturer’s paint. What is the probability that the average life of the paint for this sample will be more than 14 years? (Choose the closest value)
2. For two events, A and B, we know that P(A) = 0.2, the P(B) = 0.8 and P(A and B) = 0.05 . What is the P(A or B)?
3. The average time to complete a particular task is stated to be 150 seconds. Which of the following 95% two-sided confidence intervals on the true average time to complete the task rejects this claim?
A. 100, 148 B. 102, 198 C. 120, 178 D. 145, 185
4. A study is being conducted on the resting heart rate of long distance runners. It is believed that for a particular type of long distance runners the mean resting heart rate is believed to be 65 beats per minute (bpm) with a standard deviation of 6.2 bpm. For a random sample of 12 such runners were studied the average resting heart rate was 62 bpm with a standard deviation of 9.6 bpm. In this scenario, the value of 6.2 bpm is the
A. µ (“mu”)
C. σ (“sigma”)
D. Xbar (sample mean)
5. The sample mean is a
6. A poll is going to be taken which asks college students whether states should be allowed to conduct random drug tests on elected officials. The researcher decides to poll 389 randomly selected college students for this study. The researcher wants to estimate the proportion who agree with a 0.03 margin of error with a 90% level of confidence. For this situation, the sample size of 389 is large enough.
7. The fill volume of plastic bottles of liquid dishwashing detergent is normally distributed with a variance of 4.1 fluid ounces. If we want to estimate the average fill volume with a margin of error of 0.5 with a level of confidence of 90%, how many detergent bottles should we randomly sample?
8. The linear regression equation was relating a regressor variable, x, and a response, y. The slope was found to be 7 with intercept of 20 . What is the predicted value when x = -3?
9. A sample of 100 bugs yields an average weight of 3.6 ounces. Assuming that the population standard deviation is 0.6 ounces, find the margin of error in estimating μ (the true mean weight of all bugs of this type) at the 90 % level of confidence.
10. A group of men and women between the ages of 25 and 35 were asked “How many hours did you work last week?” We want to determine whether there is a significant difference between men and women in the mean number of hours they work each week. Sample statistics were calculated and a hypothesis test carried out. The p-value was found to be 0.04. At the 5% level of significance, which of the following statements is most appropriate?
A. There is no statistically significant difference between men and women in the mean hours they work each week.
B. There is a statistically significant difference between men and women in the mean hours they work each week.
C. There is evidence to conclude that men work more hours than women.
D. There is evidence to conclude that women work more hours than men.
11. A company must choose between two pension plans. Data was collected on hourly workers and salaried workers preference for Plan 1 (p1) and Plan 2 (p2). Right now, they are specifically interested in determining if there is a difference between the proportions of hourly workers’ preference between the two plans. Calculate the test statistic for testing the hypothesis H0: p1 – p2 = 0.
12. A company must choose between two pension plans. Data was collected on hourly workers and salaried workers preference for Plan 1 (p1) and Plan 2 (p2). Right now, they are specifically interested in determining if there is a difference between the proportions of hourly workers’ preference between the two plans. Calculate the test statistic for testing the hypothesis H0: p1 – p2 = 0.
x1= 22 n1= 30 x2= 32
13. A company is looking to replace its current measuring device for a particular product they currently manufacturer. They want to conduct a hypothesis test to determine if the “new” measuring device is identical to the old one. They randomly select 4 of these products off of the production line and measure them with the old and then the new measuring device (measurements are in millimeters (mm). The results are:
Part 1. Old device: 3.4 mm, New device: 7.0 mm;
Part 2. Old device: 3.0 mm, New device: 6.7 mm;
Part 3. Old device: 2.6 mm, New Device: 7.8 mm;
Part 4. Old device: 3.2 mm, New Device: 5.4 mm.
We want to test the claim that the new device is no different than the old one when taking measurements. Calculate the value of the test statistic for this test. Next, take the absolute value of your number. Which of the following is the absolute value of the test statistic?
B. I have no idea
14. For a particular study, at the 5% significance level, we were able to reject a null hypothesis that two population proportions were equal using a p-value. Which of the following two-sided 95% confidence intervals on the difference between two population proportions would also lead to rejection of the same null hypothesis? A. -0.067, 0.067 B. -0.090, 0.145 C. -0.113, 0.005 D. -0.130, -0.025
15. Suppose we found the correlation coefficient between two variables, X and Y, to be r = 0.95. Which of the following is most appropriate?
A. An increase in Y causes an increase in X.
B. As X increases, Y decreases.
C. As X increases, Y increases.
D. A increase in X causes an increase in Y.
16. A researcher wants to compare the average times to complete two tasks. Twelve people were selected to be in the study and each person completed both tasks. For all 12 people, the time to complete Task 1 (T1) and the time to complete Task 2 (T2) (in minutes) were recorded. After collecting the data, a 95% confidence on the difference (T1 – T2) in average time to complete the tasks was found to be (-2.4, -1.6). Which of the following interpretations is most appropriate at the 5% level of significance?
A. Based on our results, it takes longer (on average) to complete Task 1 than it does to complete Task 2
B. There is no statistically significant difference in average time to complete the tasks
C. Statistically, the average time to complete Task 1 is the same as the average time to complete Task 2
D. Based on our results, it takes longer (on average) to complete Task 2 than it does to complete Task 1
17. For a particular company, data was collected on hourly workers and salaried workers preference for two difference pension plans: Plan 1 (p1) and Plan 2 (p2). Using the table below, what is the probability that a randomly selected employee from the company will not be an hourly worker?
Job Classification Plan1 Plan2 Total
Hourly Workers 120 100 220
Salaried Workers 80 100 180
Total 200 200 400