Question 25 pts

The standard deviation of the population of airline departure delays is s 27.7 minutes. Initially we choose an SRS of 100 departures. However, we then decide that we would like to reduce the standard deviation of the sample mean by a factor of 10. What is the new sample size that we must use?

Round your answer to 2 decimal places of accuracy.

Question 36 pts

The standard deviation of the population of airline departure delays is 22 minutes. Suppose that we choose an SRS of 111 departures. Calculate the standard deviation of their mean length in minutes. Then apply the Central Limit Theorem and the 68-95-99.7 Rule to complete the following statement: "about 95% of all samples will have its mean within minutes of the true population mean p."

Round your answer to 2 decimal places of accuracy.

Question 46 pts

Consider quality control sampling of 25 watt LED lights produced by a given manufacturer. The standard deviation of the population of light lifetimes is 35.79 months. Suppose that we choose an SRS of 306 lights. Calculate the standard deviation of their mean lifetime in months. Then apply the Central Limit Theorem and the 68-95-99.7 Rule to complete the following statement: "about 99.7% of all samples will have its mean within months of the true population mean g."

Round your answer to 2 decimal places of accuracy.

Question 56 pts

Suppose that the time T between text messages sent from your cell phone is governed by the exponential distribution with mean m 13 minutes and standard deviation s 25 minutes. You record the next 50 times between sent text messages. What is the probability that their average time exceeds 10 minutes? Apply the Central Limit Theorem.

Caution: do not round at your intermediate steps. Hint: you may need to use Excel for this calculation. o 0.5000

o 0.1981

o 0.8019

o 0.3174

o 0.6826

Question 66 pts

Facebook recently examined all active Facebook users and determined that the average user has 95 Facebook friends. Suppose that the population of number of Facebook friends of a randomly selected user has a standard deviation of 259. Facebook draws a SRS of 100 Facebook users. What is the probability that the average number of Facebook friends is less than 100? Apply the Central Limit Theorem.

Caution: do not round at your intermediate steps. Hint: you may need to use Excel for this calculation.

o0.9235

o0.6826

o0.2998

o0.5765

o0.5000

Question 76 pts

The mean amount for all the invoices for your company last month is not known. Based on your past experience, you are willing to assume that the standard deviation of invoice amounts is $248. You take a random sample of 91 invoices. Apply the Central Limit

Theorem and the 68-95-99.7 Rule to complete the following sentence: "The probability is about 0.95 that the sample mean is within of the population mean p."

Enter your answer to 2 decimal places of accuracy.

Question 86 pts

You are a manager for a liquor store. Your store's computer keeps track of sales of liquor per customer. The mean amount for sales per customer last month is not known. Based on your past experience, you are willing to assume that the standard deviation of sales amounts is $48. You take a random sample of 90 sales receipts. Apply the Central Limit Theorem and the 68-95-99.7 Rule to complete the following sentence: "About 99.7% of all samples will capture the true mean of all sales, in the interval of the mean plus or minus

Enter your answer to 2 decimal places of accuracy.

Question 96 pts

In a survey conducted as an SRS of size 638, students were asked about their credit card balance. Assume that the standard deviation of the card balance among all undergraduates is $1092. Use the correct critical value z* to calculate the margin of error for the 95% confidence interval for the mean credit card debt among all undergraduates.

Enter your answer to 2 decimal places of accuracy.

Question 107 pts

Consider a sample of 1926 families selected in an SRS. The sample mean annual amount that the family paid for college was $23076. Assume that the population standard deviation for amount paid for college is $6289. Using the appropriate critical value z*, find the 90% confidence interval for the population mean for annual amount paid for college. In your answer, type the upper endpoint of this confidence interval.

Round your answer to the nearest dollar.

Question 117 pts

Consider a sample of 1187 recently graduated business majors selected in an SRS. The sample mean annual starting salary was $62984. Assume that the population standard deviation for starting salary is $11999. Using the appropriate critical value z* , find the 99% confidence interval for the population mean for annual starting salary. In your answer, type the lower endpoint of this confidence interval.

Round your answer to the nearest dollar.

Question 127 pts

Suppose that you plan to conduct an SRS of adults in the U.S., age 50 to 65, who have not yet retired. You plan to ask how much each adult has saved for retirement. Suppose that the standard deviation for amount saved for retirement is $28163. Your desired margin of error for a 95% confidence interval is $1,000. What is the smallest sample size that you need to acheive this margin of error with 95% confidence? In your calculation, use the appropriate critical value z* appropriate for a 95% confidence interval.

Round up to the nearest integer value. Note: be careful not to round at intermediate steps in your calculation.

Question 137 pts

Bestea produces a 473-milliliter (ml) bottle of sweetened green iced tea. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. Data on past production shows that the distribution of the contents is close to Normal, with standard deviation s 1.9 ml. To assess the state of the bottling process, 50 bottles were randomly selected from the streaming high volume production line. The sample mean content is found to be 472.4 ml. Is this value convincing evidence that the mean fill of all bottles produced by the current process differs from the desired level of 473 mi.?

The hypotheses: Ho: m 473 and HA: m 473. The estimate is the sample mean.

Calculate the value of the test statistic z. Enter your answer to 2 decimal places of accuracy.

Question 146 pts

Bestea produces a 473-milliliter (ml) bottle of sweetened green iced tea. There is some variation from bottle to bottle because the filling machinery is not perfectly precise. Data on past production shows that the distribution of the contents is close to Normal, with standard deviation 2.5 ml. To assess the state of the bottling process, 20 bottles were randomly selected from the streaming high volume production line. The sample mean content is found to be 474.07 ml. Is this value convincing evidence that the mean fill of all bottles produced by the current process differs from the desired level of 473 ml?

The hypotheses: Ho: 473 and HA: 473. The estimate is the sample mean.

Calculate P-value of the test. Note: you may need to use Excel to perform this calculation.

o0.0278

o0.0556

o0.0500

o0.0336

o0.0006

Question 156 pts

Starbucks serves several sizes of coffee. The Tall is 12 fluid oz. There is some variation from cup to cup because the filling machinery is not perfectly precise. Data on past production shows that the distribution of the contents is close to Normal, with standard deviation 0.6 oz. To assess the state of the filling process at a given Starbucks store, 60 cups were randomly selected over the course of a week. The sample mean content is found to be 11.87 oz. Is this value convincing evidence that the mean fill of all Tall cups of coffee produced by the current process differs from the desired level of 12.0 oz.?

The hypotheses: Ho: 12.0 and HA: 12.0. The estimate is the sample mean.

Calculate P-value of the test. Note: you may need to use Excel to perform this calculation.

o0.0933

o0.0783

o0.0500

o0.1187

o0.0466