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1) Which of the following is not a characteristic of the normal distribution? A) Symmetric B) Mean=median=mode C) Bell-shaped D) Equal probabilities at all values of x 2) Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more? A) 0.3869 B) 0.1131 C) 0.7100 D) 0.8869 3) The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. Based on this, what is the probability that a call will last longer than 13 minutes? A) About 0.0125 B) Approximately 0.4875 C) About 0.5125 D) About 0.9875 4) The actual weight of 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds. Given this information, the probability of a sack weighing more than 2.40 pounds is 0.4251. A) True B) False 5) It is thought that the time between customer arrivals at a fast food business is exponentially distributed with λ equal to 5 customers per hour. Given this information, what is the mean time between arrivals? A) 12 minutes B) 5 minutes C) 5 hours D) 2 minutes 6) If the monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00, which of the following would be the largest individual customer bill that you might expect to find? A) Approximately $811.00 B) About $195.00 C) Nearly $123.00 D) There is no way to determine this without more information. 7) Suppose the mean of dogs a pet shop grooms each day is know to be 14.2 dogs. If a sample of n = 12 days is chosen and a total of 178 dogs are groomed during those 12 days, then the sampling error is: A) 163.8. B) about 0.63. C) about -0.63. D) -163.8. 8) The population of soft drink cans filled by a particular machine is known to be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .25 ounces. Given this information, the sampling distribution for a random sample of n = 25 cans will also be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .05 ounces. A) True B) False 9) Which of the following statements is not consistent with the Central Limit Theorem? A) The Central Limit Theorem applies without regard to the size of the sample. B) The Central Limit Theorem applies to non-normal distributions. C) The Central Limit Theorem indicates that the sampling distribution will be approximately normal when the sample size is sufficiently large. D) The Central Limit Theorem indicates that the mean of the sampling distribution will be equal to the population mean. 10) A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. For a sample of 49, the probability that the sample mean will be larger than 82 is A) 0.5228 B) 0.9772 C) 0.4772 D) 0.0228 11) In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given: n = 20 = 4.33 s = 3.50 Based on this information, the upper limit for a 95 percent confidence interval estimate for the true population mean is: A) about 5.97 miles. B) about 7.83 miles. C) nearly 12.0 miles. D) about 5.86 miles. 12) In a situation where the population standard deviation is known and we wish to estimate the population mean with 90 percent confidence, what is the appropriate critical value to use? A) z = 1.96 B) z = 2.33 C) z = 1.645 D) Can’t be determined without knowing the degrees of freedom. 13 Which of the following statements is true with respect to the t-distribution? A) The t-distribution is symmetrical. B) The exact shape of the t-distribution depends on the number of degrees of freedom. C) The t-distribution is more spread out than the standard normal distribution. D) All of the above are true. 14) A major tire manufacturer wishes to estimate the mean tread life in miles for one of its tires. It wishes to develop a confidence interval estimate that would have a maximum sampling error of 500 miles with 90 percent confidence. A pilot sample of n = 50 tires showed a sample standard deviation equal to 4,000 miles. Based on this information, the required sample size is: A) 124. B) 246. C) 174. D) 196. 15) The t-distribution is used to obtain the critical value in developing a confidence interval when the population distribution is not known and the sample size is small. A) True B) False 16) Which of the following statements is true? A) The decision maker controls the probability of making a Type I statistical error. B) Alpha represents the probability of making a Type II error. C) Alpha and beta are directly related such that when one is increased the other will increase also. D) The alternative hypothesis should contain the equality. 17) If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110. A) less than B) greater than C) equal to D) not comparable to 18) A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, which of the following would be the upper tail critical value? A) 1.28 B) 1.645 C) 1.96 D) 2.575 19) When testing a two-tailed hypothesis using a significance level of 0.05, a sample size of n = 16, and with the population standard deviation unknown, which of the following is true? A) The null hypothesis can be rejected if the sample mean gets too large or too small compared with the hypothesized mean. B) The alpha probability must be split in half and a rejection region must be formed on both sides of the sampling distribution. C) The test statistic will be a t-value. D) All of the above are true. 20) Which of the following statements is true? A) The decision maker controls the probability of making a Type I statistical error. B) Alpha represents the probability of making a Type II error. C) Alpha and beta are directly related such that when one is increased the other will increase also. D) The alternative hypothesis should contain the equality. 21) Suppose that a group of 10 people join a weight loss program for 3 months. Each person’s weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as: A) independent samples using the normal distribution. B) paired samples using the t-distribution. C) independent samples using the t-distribution. D) independent proportions. 22) If the population variances are assumed to be known in an application where a manager wishes to estimate the difference between two population means, the 95 percent confidence interval estimate can be developed using which of the following critical values: A) z = 1.645. B) z = 1.96. C) t value that depends on the sample sizes from the two populations. D) z = 2.575. 23) If we are testing for the difference between the means of two independent populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to: A) 39. B) 38. C) 19. D) 18. 24) Suppose that a group of 10 people join a weight loss program for 3 months. Each person’s weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as: A) independent samples using the normal distribution. B) paired samples using the t-distribution. C) independent samples using the t-distribution. D) independent proportions. Optional (extra credit) 25) Which of the following statements is true with respect to the sampling distribution of a proportion? A) An increase in the sample size will result in a reduction in the size of the standard deviation. B) As long as the sample size is sufficiently large, the sampling distribution will be approximately normal. C) The mean of the sampling distribution will equal the population proportion. D) All of the above are true. 26) In determining the sample size requirement for an application involving the estimation of the proportion of department store customers who pay using the store’s credit card, the closer the true proportion is to .5, the larger will be the required sample size for a given margin of error and confidence level. A) True B) False 27) When the hypothesized proportion is close to 0.50, the spread in the sampling distribution of p is greater than when the hypothesized proportion is close to 0.0 or 1.0. A) True B) False 28) An advertising company has developed a new ad for one of the national car manufacturing companies. The ad agency is interested in testing whether the proportion of favorable responses to the ad is the same between male adults versus female adults. It plans on conducting the test using an alpha level equal to 0.05. A sample of 100 adults of each gender will be used in the study. Each person will be asked to view the ad and indicate whether they find the ad to be “pleasing” or not. Given this, what is the appropriate null hypothesis?

1) Which of the following is not a characteristic of the normal distribution?

A) Symmetric

B) Mean=median=mode

C) Bell-shaped

D) Equal probabilities at all values of x

2) Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33. Based on this information, what is the probability that a randomly selected stock will close up $.75 or more?

A) 0.3869

B) 0.1131

C) 0.7100

D) 0.8869

3) The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes. Based on this, what is the probability that a call will last longer than 13 minutes?

A) About 0.0125

B) Approximately 0.4875

C) About 0.5125

D) About 0.9875

4) The actual weight of 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds. Given this information, the probability of a sack weighing more than 2.40 pounds is 0.4251.

 

A) True

B) False

5) It is thought that the time between customer arrivals at a fast food business is exponentially distributed with λ equal to 5 customers per hour. Given this information, what is the mean time between arrivals?

A) 12 minutes

B) 5 minutes

C) 5 hours

D) 2 minutes

6) If the monthly electrical utility bills of all customers for the Far East Power and Light Company are known to be distributed as a normal distribution with mean equal to $87.00 a month and standard deviation of $36.00, which of the following would be the largest individual customer bill that you might expect to find?

A) Approximately $811.00

B) About $195.00

C) Nearly $123.00

D) There is no way to determine this without more information.

7) Suppose the mean of dogs a pet shop grooms each day is know to be 14.2 dogs. If a sample of n = 12 days is chosen and a total of 178 dogs are groomed during those 12 days, then the sampling error is:

A) 163.8.

B) about 0.63.

C) about -0.63.

D) -163.8.

8) The population of soft drink cans filled by a particular machine is known to be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .25 ounces. Given this information, the sampling distribution for a random sample of n = 25 cans will also be normally distributed with a mean equal to 12 ounces and a standard deviation equal to .05 ounces.

A) True

B) False

9) Which of the following statements is not consistent with the Central Limit Theorem?

A) The Central Limit Theorem applies without regard to the size of the sample.

B) The Central Limit Theorem applies to non-normal distributions.

C) The Central Limit Theorem indicates that the sampling distribution will be approximately normal when the sample size is sufficiently large.

D) The Central Limit Theorem indicates that the mean of the sampling distribution will be equal to the population mean.

10) A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. For a sample of 49, the probability that the sample mean will be larger than 82 is

A) 0.5228

B) 0.9772

C) 0.4772

D) 0.0228

11) In an application to estimate the mean number of miles that downtown employees commute to work roundtrip each day, the following information is given:

n = 20

= 4.33

s = 3.50

Based on this information, the upper limit for a 95 percent confidence interval estimate for the true population mean is:

A) about 5.97 miles.

B) about 7.83 miles.

C) nearly 12.0 miles.

D) about 5.86 miles.

12) In a situation where the population standard deviation is known and we wish to estimate the population mean with 90 percent confidence, what is the appropriate critical value to use?

A) z = 1.96

B) z = 2.33

C) z = 1.645

D) Can’t be determined without knowing the degrees of freedom.

13 Which of the following statements is true with respect to the t-distribution?

A) The t-distribution is symmetrical.

B) The exact shape of the t-distribution depends on the number of degrees of freedom.

C) The t-distribution is more spread out than the standard normal distribution.

D) All of the above are true.

14) A major tire manufacturer wishes to estimate the mean tread life in miles for one of its tires. It wishes to develop a confidence interval estimate that would have a maximum sampling error of 500 miles with 90 percent confidence. A pilot sample of n = 50 tires showed a sample standard deviation equal to 4,000 miles. Based on this information, the required sample size is:

A) 124.

B) 246.

C) 174.

D) 196.

15) The t-distribution is used to obtain the critical value in developing a confidence interval when the population distribution is not known and the sample size is small.

A) True

B) False

16) Which of the following statements is true?

A) The decision maker controls the probability of making a Type I statistical error.

B) Alpha represents the probability of making a Type II error.

C) Alpha and beta are directly related such that when one is increased the other will increase also.

D) The alternative hypothesis should contain the equality.

17) If we are performing a two-tailed test of whether μ = 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

A) less than

B) greater than

C) equal to

D) not comparable to

18) A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, which of the following would be the upper tail critical value?

A) 1.28

B) 1.645

C) 1.96

D) 2.575

19) When testing a two-tailed hypothesis using a significance level of 0.05, a sample size of n = 16, and with the population standard deviation unknown, which of the following is true?

A) The null hypothesis can be rejected if the sample mean gets too large or too small compared with the hypothesized mean.

B) The alpha probability must be split in half and a rejection region must be formed on both sides of the sampling distribution.

C) The test statistic will be a t-value.

D) All of the above are true.

20) Which of the following statements is true?

A) The decision maker controls the probability of making a Type I statistical error.

B) Alpha represents the probability of making a Type II error.

C) Alpha and beta are directly related such that when one is increased the other will increase also.

D) The alternative hypothesis should contain the equality.

21) Suppose that a group of 10 people join a weight loss program for 3 months. Each person’s weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as:

A) independent samples using the normal distribution.

B) paired samples using the t-distribution.

C) independent samples using the t-distribution.

D) independent proportions.

22) If the population variances are assumed to be known in an application where a manager wishes to estimate the difference between two population means, the 95 percent confidence interval estimate can be developed using which of the following critical values:

A) z = 1.645.

B) z = 1.96.

C) t value that depends on the sample sizes from the two populations.

D) z = 2.575.

23) If we are testing for the difference between the means of two independent populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to:

A) 39.

B) 38.

C) 19.

D) 18.

24) Suppose that a group of 10 people join a weight loss program for 3 months. Each person’s weight is recorded at the beginning and at the end of the 3-month program. To test whether the weight loss program is effective, the data should be treated as:

A) independent samples using the normal distribution.

B) paired samples using the t-distribution.

C) independent samples using the t-distribution.

D) independent proportions.

Optional (extra credit)

25) Which of the following statements is true with respect to the sampling distribution of a proportion?

A) An increase in the sample size will result in a reduction in the size of the standard deviation.

B) As long as the sample size is sufficiently large, the sampling distribution will be approximately normal.

C) The mean of the sampling distribution will equal the population proportion.

D) All of the above are true.

26) In determining the sample size requirement for an application involving the estimation of the proportion of department store customers who pay using the store’s credit card, the closer the true proportion is to .5, the larger will be the required sample size for a given margin of error and confidence level.

A) True

B) False

27) When the hypothesized proportion is close to 0.50, the spread in the sampling distribution of p is greater than when the hypothesized proportion is close to 0.0 or 1.0.

A) True

B) False

28) An advertising company has developed a new ad for one of the national car manufacturing companies. The ad agency is interested in testing whether the proportion of favorable responses to the ad is the same between male adults versus female adults. It plans on conducting the test using an alpha level equal to 0.05. A sample of 100 adults of each gender will be used in the study. Each person will be asked to view the ad and indicate whether they find the ad to be “pleasing” or not. Given this, what is the appropriate null hypothesis?

 

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