Practice Test 3 Business Statistics

Practice Test 3 Business Statistics:

Name:______Date:______

Multiple Choice: Each is worth two points Identify the letter of the choice that best completes the statement or answers the question.

____ 1. The ability of an interval estimate to contain the value of the population parameter is described by the a. confidence level b. degrees of freedom c. precise value of the population mean  d. degrees of freedom minus 1 ____ 2. In general, higher confidence levels provide a. wider confidence intervals b. narrower confidence intervals c. a smaller standard error d. unbiased estimates

Exhibit 8-2 A random sample of 81 automobiles traveling on an interstate showed an average speed of 60 mph and a standard deviation of 13.5 mph. Assume the distribution of speeds of all the cars is normal.

____ 3. Refer to Exhibit 8-2. If we are interested in determining an interval estimate for  at 86.9% confidence, the Z value to use is a. 1.96 b. 1.31 c. 1.51 d. 2.00 ____ 4. If we are interested in testing whether the mean of population 1 is smaller than the mean of population 2, the

a. null hypothesis should state 1 - 2 < 0

b. null hypothesis should state 1 - 2 > 0

c. alternative hypothesis should state 1 - 2  0

d. alternative hypothesis should state 1 - 2  0 ____ 5. Independent samples are obtained from two normal populations with equal variances in order to construct a confidence interval estimate for the difference between the population means. If the first sample contains 16 items and the second sample contains 36 items, the correct form to use for the sampling distribution is the a. normal distribution b. t distribution with 15 degrees of freedom c. t distribution with 35 degrees of freedom d. t distribution with 50 degrees of freedom

1 Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG (miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test.

Driver Manufacturer A Manufacturer B 1 29 27 2 24 23 3 26 28 4 24 23 5 25 24 6 27 26 7 30 28 8 25 27

____ 6. Refer to Exhibit 10-9. The test statistic is a. 1.96 b. 0.884 c. 2.75 d. 0.095

____ 7. If two independent large samples are taken from two populations, the sampling distribution of the difference between the two sample proportions a. can be approximated by a Poisson distribution b. will have a standard error of proportion of one c. can be approximated by a normal distribution d. will have a proportion of 50%

Exhibit 11-1 In a random sample of 60 men, 42 reported that they were in favor of team A to win the Superbowl, while in a sample of 100 women 77 favored team A to win.

____ 8. Refer to Exhibit 11-1. The standard error of the difference between the two proportions is a. - 0.50 b. - 0.0726 c. 0.0726 d. 0.212

____ 9. A weatherman stated that the average temperature during July in Chattanooga is more than 80 degrees. A sample of 32 months of July is taken. The correct set of hypotheses is

a. H0:   80 Ha:   80

b. H0:   80 Ha:  > 80

c. H0:   80 Ha:  = 80

d. H0:  < 80 Ha:  > 80

Exhibit 9-2

n = 16 = 75.76 s = 8.246 H0:   80

2 Ha:  < 80

____ 10. Refer to Exhibit 9-2. If the test is done at the 1% level of significance, the null hypothesis should a. not be rejected b. be rejected c. Not enough information is given to answer this question. d. None of these alternatives is correct.

Exhibit 9-3

n = 49 = 54.8 s = 28 H0:  = 50

Ha:   50

____ 11. Refer to Exhibit 9-3. If the test is done at the 5% level of significance, the null hypothesis should a. not be rejected b. be rejected c. Not enough information given to answer this question. d. None of these alternatives is correct.

____ 12. For a one-tailed test (lower tail) at 89.8% confidence, Z = a. -1.27 b. -1.53 c. -1.96 d. -1.64 ____ 13. For a one-tailed test (upper tail), a sample size of 26 at 90% confidence, t = a. 1.316 b. -1.316 c. -1.740 d. 1.740

____ 14. As the sample size increases, the margin of error a. increases b. decreases c. stays the same d. None of the other answers are correct.

____ 15. The ability of an interval estimate to contain the value of the population parameter is described by the a. confidence level b. degrees of freedom c. precise value of the population mean μ d. None of the other answers are correct.

____ 16. If an interval estimate is said to be constructed at the 90% confidence level, the confidence coefficient would be a. 0.1 b. 0.95 c. 0.9 d. 0.05

3 Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph and a standard deviation of 13.5 mph. Assume the distribution of speeds of all the cars is normal.

____ 17. Refer to Exhibit 8-3. If we are interested in determining an interval estimate for μ at 86.9% confidence, the z value to use is a. 1.96 b. 1.31 c. 1.51 d. 2.00

____ 18. Refer to Exhibit 8-3. The value to use for the standard error of the mean is a. 13.5 b. 9 c. 2.26 d. 1.5

____ 19. Refer to Exhibit 8-3. The 86.9% confidence interval for μ is a. 46.500 to 73.500 b. 57.735 to 62.625 c. 59.131 to 60.869 d. 50 to 70

____ 20. In hypothesis testing, the alternative hypothesis is a. the hypothesis tentatively assumed true in the hypothesis-testing procedure b. the hypothesis concluded to be true if the null hypothesis is rejected c. the maximum probability of a Type I error d. All of these answers are correct.

____ 21. Your investment executive claims that the average yearly rate of return on the stocks she recommends is at least 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is

a. H0:  < 10.0% Ha:   10.0%

b. H0:   10.0% Ha:  > 10.0%

c. H0:  > 10.0% Ha:   10.0%

d. H0:   10.0% Ha:  < 10.0%

____ 22. A Type II error is committed when a. a true alternative hypothesis is mistakenly rejected b. a true null hypothesis is mistakenly rejected c. the sample size has been too small d. not enough information has been available

____ 23. The probability of making a Type I error is denoted by a.  b.  c. 1 -  d. 1 - 

4 Exhibit 9-1

n = 36 x = 24.6 s = 12 H0:   20 Ha:  > 20

____ 24. Refer to Exhibit 9-1. The test statistic equals a. 2.3 b. 0.38 c. -2.3 d. -0.38

____ 25. Refer to Exhibit 9-1. The p-value is a. 0.5107 b. 0.0214 c. 0.0107 d. 2.1

____ 26. Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should a. not be rejected b. be rejected c. Not enough information is given to answer this question. d. None of the other answers are correct.

5 Short Answer Problems

Directions: Clearly designate the solution to each problem. Make sure to show all work/method to ensure you receive full credit.

1.Twenty percent of the applications received for a particular position are rejected. What is the probability that among the next fourteen applications, a. none will be rejected? b. all will be rejected? c. less than 2 will be rejected? d. more than four will be rejected? e. Determine the expected number of rejected applications and its variance.

6 2.It is known that the variance of a population equals 484. A random sample of 81 observations is going to be taken from the population. a. With a .80 probability, what statement can be made about the size of the margin of error? b. With a .80 probability, how large of a sample would have to be taken to provide a margin of error of 3 or less?

3.In order to determine whether or not a driver's education course improves the scores on a driving exam, a sample of 6 students were given the exam before and after taking the course. The results are shown below. Let d = Score After - Score Before.

Score Score Student Before the Course After the Course 1 83 87 2 89 88 3 93 91 4 77 77 5 86 93 6 79 83

Use  = 0.1 and test to see if taking the course actually increased scores on the driving exam.

7 4.Consider the following results for two samples randomly taken from two populations.

Sample A Sample B Sample Size 11 15 Sample Mean 24 22 Sample Standard Deviation 5 6

a. Determine the pooled estimate of the population variance. b. Develop a 95% confidence interval for the difference between the two population means.

5.In order to estimate the average electric usage per month, a sample of 196 houses was selected, and the electric usage determined. a. Assume a population standard deviation of 350 kilowatt hours. Determine the standard error of the mean. b. With a 0.95 probability, determine the margin of error. c. If the sample mean is 2,000 KWH, what is the 95% confidence interval estimate of the population mean?

8 6.A random sample of 100 credit sales in a department store showed an average sale of $120.00. From past data, it is known that the standard deviation of the population is $40.00. a. Determine the standard error of the mean. b. With a 0.95 probability, determine the margin of error. c. What is the 95% confidence interval of the population mean?