Fry Brothers Heating andAir Conditioning Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?

Given the following hypothesis: A random sample of five resulted in the following values: 18, 15, 12, 19, and 21.Assume a normal population. Using the .01 significance level, can we conclude the population mean is less than 20? a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis? d. Estimate the p-value

$$H_0:μ≥20; H_1:μ<20$$

(a) Interpret: What does Antigone mean when she says, "Your edict, King, was strong, / But all your strength is weakness itself against / The immortal unrecorded laws of God"?

(b) Compare and Contrast: Compare Antigone's position with Creon's.

According to the local union president, the mean gross income of plumbers in the Salt Lake City area follows the normal probability distribution with a mean of $45,000 and a standard deviation of$3,000. A recent investigative reporter for KYAK TV found, for a sample of 120 plumbers, the mean gross income was $45,500. At the .10 significance level, is it reasonable to conclude that the mean income is not equal to$45,000? Determine the p-value

A recent study of 26 Conway, SC, residents revealed they had lived at their current address an average of 9.3 years. The standard deviation of the sample was 2 years. a. What is the population mean? b. What is the best estimate of the population mean? c. What is the standard error of estimate? d. Develop a 90 percent confidence interval for the population mean.

Clark Heter is an industrial engineer at LyonsProducts. He would like to determine whether there are more units produced on the night shift than on the day shift. Assume the population standard deviation for the number of units produced on the day shift is 21 and is 28 on the night shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345. A sample of 60 night-shift workers showed that the mean number of units produced was 351. At the .05 significance level, is the number of units produced on the night shift larger?

A tire manufacturer wishes to investigate the tread life of its tires. A sample of 10 tires driven 50,000 miles revealed a sample mean of 0.32 inch of tread remaining with a standard deviation of 0.09 inch. Construct a 95 percent confidence interval for the population mean. Would it be reasonable for the manufacturer to conclude that after 50, 000 miles mean amount of tread remaining is 0.30 inches?

The owner of Bun ‘N’ Run Hamburgers wishes to compare the sales per day at two locations. The mean number sold for 10 randomly selected days at the Northside site was 83.55, and the standard deviation was 10.50. For a random sample of 12 days at the Southside location, the mean number sold was 78.80 and the standard deviation was 14.25. At the .05 significance level, is there a difference in the mean number of hamburgers sold at the two locations? What is the p-value?

Do married and unmarried women spend the same amount of time per week using Facebook? A random sample of 45 married women who use Facebook spent an average of 3.0 hours per week on this social media website. A random sample of 39 unmarried women who regularly use Facebook spent an average of 3.4 hours per week. Assume that the weekly Facebook time for married women has a population standard deviation of 1.2 hours, and the population standard deviation for unmarried, regular Facebook users is 1.1 hours per week. Using the .05 significance level, do married and unmarried women differ in the amount of time per week spent on Facebook? Find the p-value and interpret the result.

Are nursing salaries in Tampa, Florida, lower than those in Dallas, Texas? Salary data show staff nurses in Tampa earn less than staff nurses in Dallas (The Tampa Tribune, January 15, 2007). Suppose that in a follow-up study of 40 staff nurses in Tampa and 50 staff nurses in Dallas you obtain the following results.

$$\begin{array} { r l } { \text { Tampa } } & { \text { Dallas } } \\ { n _ { 1 } = 40 } & { n _ { 2 } = 50 } \\ { \overline { x } _ { 1 } = \$ 56,100 } & { \overline { x } _ { 2 } = \$ 59,400 } \\ { s _ { 1 } = \$ 6000 } & { s _ { 2 } = \$ 7000 } \end{array}$$

Formulate hypothesis so that, if the null hypothesis is rejected, we can conclude that salaries for staff nurses in Tampa are significantly lower than for those in Dallas. Use $\alpha$= .05.

Mary Jo Fitzpatrick is the vice president for Nursing Services at St. Luke’s Memorial Hospital. Recently she noticed in the job postings for nurses that those that are unionized seem to offer higher wages. She decided to investigate and gathered the following information.

$$\begin{array}{|lccc|} \hline \text { Group } & \text { Sample Size } & \text { Sample } & \text { Population } \\ \text { Union } & 40 & \$ 20.75 & \$ 2.25 \\ \text { Nonunion } & 45 & \$ 19.80 & \$ 1.90 \\ \hline \end{array}$$

Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is the p-value?

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.

$$\begin{array}{|lcc|} \hline \text { Statistic } & \text { Men } & \text { Women } \\ \hline \text { Sample mean } & 24.51 & 22.69 \\ \text { Sample standard deviation } & 4.48 & 3.86 \\ \text { Sample size } & 35 & 40 \\ \hline \end{array}$$

At the .01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month? What is the p-value?

A recent study compared the time spent together by single- and dual-earner couples. According to the records kept by the wives during the study, the mean amount of time spent together watching television among the single-earner couples was 61 minutes per day, with a standard deviation of 15.5 minutes. For the dual-earner couples, the mean number of minutes spent watching television was 48.4 minutes, with a standard deviation of 18.1 minutes. At the .01 significance level, can we conclude that the single-earner couples on average spend more time watching television together? There were 15 singleearner and 12 dual-earner couples studied.

A recent study revealed the typical American coffee drinker consumes an average of 3.1 cups per day. A sample of 12 senior citizens revealed they consumed the following amounts of coffee, reported in cups, yesterday.

$$\begin{array}{llllllllllll} 3.1 & 3.3 & 3.5 & 2.6 & 2.6 & 4.3 & 4.4 & 3.8 & 3.1 & 4.1 & 3.1 & 3.2 \end{array}$$

At the .05 significance level, do these sample data suggest there is a difference between the national average and the sample mean from senior citizens?