1- A random sample of the amount paid (in dollars) for taxi fare from downtown to the airport was obtained. (Give your answers correct to two decimal places.)

23

18

22

15

22

19

19

13

13

19

19

12

16

12

16

(a) Use the data to find a point estimate for the mean. $ (b) Use the data to find a point estimate for the variance. $ (c) Use the data to find a point estimate for the standard deviation. $

2- The number of engines owned per fire department was obtained from a random sample taken from profiles of fire departments from across the United States. (Give your answers correct to two decimal places.)

36

41

8

30

26

11

49

9

52

15

50

26

(a) Use the data to find a point estimate for the mean. engines (b) Use the data to find a point estimate for the variance. (c) Use the data to find a point estimate for the standard deviation. engines

3- The sampled population is normally distributed, with the given information. (Round your answers to two decimal places.)n = 19, x = 29.3, and = 6.2 (a) Find the 0.95 confidence interval for . ............. to .............. (b) Are the assumptions satisfied? Explain.

• Yes, the sampled population is normally distributed.
• No, the sample distribution is not normally distributed.
• Not enough information

4- Consider a sampled population that is normally distributed, with the given information. (Give your answers correct to two decimal places.)n = 59, x = 77.9, and = 12.7 (a) Find the 0.98 confidence interval for . .............. to .............. (b) Are the assumptions satisfied? Explain.Yes, the sample size is large enough to apply the CLT.No, the sample size is not large enough to apply the CLT. not enough information

5- How large a sample should be taken if the population mean is to be estimated with 99% confidence to within $84? The population has a standard deviation of $900. (Round your answer up to the next whole number.) ...........

6- The new mini-laptop computers can deliver as much computing power as machines several times their size, but they weigh in at less than 3 lb. How large a sample would be needed to estimate the population mean weight if the maximum error of estimate is to be 0.49 of 1 standard deviation with 98% confidence? (Round you answer up to the nearest whole number.)

7- Consider the following.(a) If is assigned the value 0.001, what are we saying about the type I error?

• very serious
• somewhat serious
• not at all serious
• not enough information

(b) If is assigned the value 0.05, what are we saying about the type I error?very serious

• somewhat serious
• not at all serious
• not enough information

(c) If is assigned the value 0.10, what are we saying about the type I error?

• very serious
• somewhat serious
• not at all serious
• not enough information

8- Consider the following. (Round your answers to four decimal places.)

(a) Calculate the p-value for H₀: = 20, H_a: < 20; x = 17.4, = 9.2, n = 22. (b) Calculate the p-value for H₀: = 78.5, H_a: > 78.5; x = 81.4, = 16, n = 24. (c) Calculate the p-value for H₀: = 1.587, H_a: 1.587; x = 1.611, = 0.32, n = 26.

9- The owner of a local chain of grocery stores is always trying to minimize the time it takes her customers to check out. In the past, she has conducted many studies of the checkout times, and they have displayed a normal distribution with a mean time of 12.4 minutes. and a standard deviation of 2.4 minutes. She has implemented a new schedule for cashiers in hopes of reducing the mean checkout time. A random sample of 32 customers visiting her store this week resulted in a mean of 11 minutes. Does she have sufficient evidence to claim the mean checkout time this week was less than 12.4 minutes? Use = 0.02.(a) Find z. (Round your answer to two decimal places.) (ii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion.

• Reject the null hypothesis. There is not significant evidence that the mean checkout time is less than 12.4 minutes.
• Reject the null hypothesis. There is significant evidence that the mean checkout time is less than 12.4 minutes.
• Fail to reject the null hypothesis. There is not significant evidence that the mean checkout time is less than 12.4 minutes.
• Fail to reject the null hypothesis. There is significant evidence that the mean checkout time is less than 12.4 minutes.

10- If the sample data produce a test statistic (z-score) that is in the critical region, then which of the following is the appropriate conclusion for the test?

• reject H₁
• reject H₀
• fail to reject H₁
• fail to reject H₀

11-The null hypothesis always concerns a population even though the data come from a sample.

True or False

12- Construct a 98% confidence interval estimate for the mean using the given sample information. (Give your answers correct to two decimal places.)n = 23, x = 17.4, and s = 2.3

............ to .........

13- The pulse rates for 13 adult women were as follows. Construct a 0.99 confidence interval for the mean pulse rate. (Give your answers correct to one decimal place.)

56

61

67

78

64

63

78

89

60

59

99

72

66

Lower limit
Upper limit

14- The addition of a new accelerator is claimed to decrease the drying time of latex paint by more than 4%. Several test samples were conducted with the following percentage decrease in drying time. Assume that the percentage decrease in drying time is normally distributed.

5.3

6.5

3.6

5.7

3.2

2.0

2.3

3.7

(a) Find the 95% confidence interval for the true mean decrease in the drying time based on this sample. (Give your answers correct to two decimal places.) .......... to .............. (b) Do you think these percentages average 4 or more? These percentages ---Select--- to average very closely to 4%

does not seem

seem to average

15- State the null hypothesis, H_o, and the alternative hypothesis, H_a, that would be used to test each of the following claims.(a) The mean weight of honeybees is at least 11 grams.

Ho:	---Select--- equal to ; greater than ; less than ; not equal to 11
Ha:	---Select--- equal to ; greater than ; less than ; not equal to 11

(b) The mean age of patients at Memorial Hospital is no more than 54 years.

Ho:	---Select--- equal to ; greater than ; less than ; not equal to 54
Ha:	---Select--- equal to ; greater than ; less than ; not equal to 54

(c) The mean amount of salt in granola snack bars is 75 mg.

Ho:	---Select--- equal to ; greater than ; less than ; not equal to 75
Ha:	---Select--- equal to ; greater than ; less than ; not equal to 75

16- Use a computer or calculator to find the p-value for the hypothesis test. (Give your answer correct to three decimal places.)

H_o: = 32, H_a: > 32, n = 18, x = 32.71, s = 2.8

17- A student group maintains that each day, the average student must travel for at least 25 minutes one way to reach college. The college admissions office obtained a random sample of 35 one-way travel times from students. The sample had a mean of 20.3 minutes and a standard deviation of 9.1 minutes. Does the admissions office have sufficient evidence to reject the students' claim? Use = 0.01.(a) State the appropriate null and alternative hypotheses. H₀: ? 25

(select for ?) = > < H_a: ? 25 (select for ?) = > <

(ii) Find t. (Round your answer to two decimal places.) (iii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion.

• Reject the null hypothesis. There is not significant evidence that the mean travel time is less than 25 minutes.
• Reject the null hypothesis. There is significant evidence that the mean travel time is less than 25 minutes.
• Fail to reject the null hypothesis. There is not significant evidence that the mean travel time is less than 25 minutes.
• Fail to reject the null hypothesis. There is significant evidence that the mean travel time is less than 25 minutes.

18- A bank randomly selected 260 checking account customers and found that 111 of them also had savings accounts at this same bank. Construct a 95% confidence interval for the true proportion of checking account customers who also have savings accounts. (Round your answers to three decimal places.)

lower limit
upper limit

19- A politician claims that she will receive at least 63% of the vote in an upcoming election. The results of a properly designed random sample of 100 voters showed that 56 of those sampled will vote for her. Is it likely that her assertion is correct at the 0.05 level of significance?(a) State the appropriate null and alternative hypotheses. H₀: p ? 0.63

(select for ?) = > < H_a: p ? 0.63

(select for ?) = > < (ii) Find z. (Round your answer to two decimal places.) (iii) Find the p-value. (Round your answer to four decimal places.) (b) State the appropriate conclusion.

• Fail to reject the null hypothesis, there is not significant evidence that she will receive less than 63% of the vote.
• Fail to reject the null hypothesis, there is significant evidence that she will receive less than 63% of the vote.
• Reject the null hypothesis, there is significant evidence that she will receive less than 63% of the vote.
• Reject the null hypothesis, there is not significant evidence that she will receive less than 63% of the vote.

20- Find n for a 95% confidence interval for p with E = 0.033 using an estimate of p = 0.2. (Round up to the nearest whole number.)