Chapter 10

(a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding \(H_{0} ?\) (e) What is the \(p\) -value? Interpret it. The following information is available. \(H_{0}: \mu=50\) \(H_{i}: \mu \neq 50\) The sample mean is \(49,\) and the sample size is \(36 .\) The population standard deviation is 5\. Use the .05 significance level.

(a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding \(H_{0} ?\) (e) What is the \(p\) -value? Interpret it. A sample of 36 observations is selected from a normal population. The sample mean is \(21,\) and the population standard deviation is \(5 .\) Conduct the following test of hypothesis using the .05 significance level. $$\begin{array}{l}H_{0}: \mu \leq 20 \\\H_{1}: \mu>20\end{array}$$

(a) Is this a one- or two-tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding \(H_{0} ?\) (e) What is the \(p\) -value? Interpret it. A sample of 64 observations is selected from a normal population. The sample mean is \(215,\) and the population standard deviation is \(15 .\) Conduct the following test of hypothesis using the .03 significance level.$$\begin{array}{l}H_{0} ; \mu \geq 220 \\\H_{1}: \mu<220\end{array}$$

The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. The population standard deviation of the mileage is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59,500 miles. Is Crosset's experience different from that claimed by the manufacturer at the .05 significance level?

The MacBurger restaurant chain claims that the mean waiting time of customers is 3 minutes with a population standard deviation of 1 minute. The quality- assurance department found in a sample of 50 customers at the Warren Road MacBurger that the mean waiting time was 2.75 minutes. At the .05 significance level, can we conclude that the mean waiting time is less than 3 minutes?

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, "You can average more than \(\$ 80\) a day in tips." Assume the standard deviation of the population distribution is 3.24 . Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was 84.85 . At the .01 significance level, can Ms. Brigden conclude that she is earning an average of more than 80 in tips?

Given the following hypothesis: $$\begin{array}{l}H_{0}: \mu \leq 10 \\\H_{1}: \mu>10\end{array}$$ For a random sample of 10 observations, the sample mean was 12 and the sample standard deviation \(3 .\) Using the .05 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis?

Given the following hypothesis: $$\begin{aligned}H_{0}: \mu &=400 \\\H_{1}: \mu & \neq 400\end{aligned}$$ For a random sample of 12 observations, the sample mean was 407 and the sample standard deviation \(6 .\) Using the .01 significance level: a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis?

The Rocky Mountain district sales manager of Rath Publishing, Inc., a college textbook publishing company, claims that the sales representatives make an average of 40 sales calls per week. Several reps say that this estimate is too low. To investigate, a random sample of 28 sales representatives reveals that the mean number of calls made last week was \(42 .\) The standard deviation of the sample is 2.1 calls. Using the .05 significance level, can we conclude that the mean number of calls per salesperson per week is more than \(40 ?\)

The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

A spark plug manufacturer claimed that its plugs have a mean life in excess of 22,100 miles. Assume the life of the spark plugs follows the normal distribution. A fleet owner purchased a large number of sets. A sample of 18 sets revealed that the mean life was 23,400 miles and the standard deviation was 1,500 miles. Is there enough evidence to substantiate the manufacturer's claim at the .05 significance level?

Given the following hypothesis: $$\begin{array}{l}H_{0}: \mu \geq 20 \\\H_{1}: \mu<20\end{array}$$ A random sample of five resulted in the following values: \(18,15,12,19,\) and \(21 .\) 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.

Given the following hypothesis: $$\begin{array}{l}H_{i} ; \mu=100 \\\H_{1}: \mu \neq 100\end{array}$$ A random sample of six resulted in the following values: 118 \(105,112,119,105,\) and \(111 .\) Using the .05 significance level, can we conclude the mean is different from \(100 ?\) 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.

Experience raising New Jersey Red chickens revealed the mean weight of the chickens at five months is 4.35 pounds. The weights follow the normal distribution. In an effort to increase their weight, a special additive is added to the chicken feed. The subsequent weights of \(a\) sample of five-month- old chickens were (in pounds): $$\begin{array}{|lllllllll|}\hline 4.41 & 4.37 & 4.33 & 4.35 & 4.30 & 4.39 & 4.36 & 4.38 & 4.40 & 4.39 \\\\\hline\end{array}$$ At the .01 level, has the special additive increased the mean weight of the chickens? Estimate the \(p\) -value.

The liquid chlorine added to swimming pools to combat algae has a relatively short shelf life before it loses its effectiveness. Records indicate that the mean shelf life of a 5 -gallon jug of chlorine is 2,160 hours (90 days). As an experiment, Holdlonger was added to the chlorine to find whether it would increase the shelf life. A sample of nine jugs of chlorine had these shelf lives (in hours): $$\begin{array}{|lllllllll|}\hline 2,159 & 2,170 & 2,180 & 2,179 & 2,160 & 2,167 & 2,171 & 2,181 & 2,185 \\\\\hline\end{array}$$ At the .025 level, has Holdlonger increased the shelf life of the chlorine? Estimate the \(p\) -value.

Hugger Polls contends that an agent conducts a mean of 53 in-depth home surveys every week. A streamlined survey form has been introduced, and Hugger wants to evaluate its effectiveness. The number of in-depth surveys conducted during a week by a random sample of agents are: $$\begin{array}{|lllllllllllllll|}\hline 53 & 57 & 50 & 55 & 58 & 54 & 60 & 52 & 59 & 62 & 60 & 60 & 51 & 59 & 56 \\\\\hline\end{array}$$ At the .05 level of significance, can we conclude that the mean number of interviews conducted by the agents is more than 53 per week? Estimate the \(p\) -value.

The following hypotheses are given. $$\begin{aligned}H_{0}: & \pi \leq .70 \\\H_{1}: & \pi>.70\end{aligned}$$ A sample of 100 observations revealed that \(p=.75 .\) At the .05 significance level, can the null hypothesis be rejected? a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis?

The following hypotheses are given. $$\begin{array}{l}H_{0}: \pi=.40 \\\H_{1}: \pi \neq .40\end{array}$$ A sample of 120 observations revealed that \(p=.30\). At the .05 significance level, can the null hypothesis be rejected? a. State the decision rule. b. Compute the value of the test statistic. c. What is your decision regarding the null hypothesis? Note: It is recommended that you use the five-step hypothesis-testing procedure in solving the following problems.

The National Safety Council reported that 52 percent of American turnpike drivers are men. A sample of 300 cars traveling southbound on the New Jersey Turnpike yesterday revealed that 170 were driven by men. At the .01 significance level, can we conclude that a larger proportion of men were driving on the New Jersey Turnpike than the national statistics indicate?

A recent article in USA Today reported that a job awaits only one in three new college graduates. The major reasons given were an overabundance of college graduates and a weak economy. A survey of 200 recent graduates from your school revealed that 80 students had jobs. At the .02 significance level, can we conclude that a larger proportion of students at your school have jobs?

Chicken Delight claims that 90 percent of its orders are delivered within 10 minutes of the time the order is placed. A sample of 100 orders revealed that 82 were delivered within the promised time. At the .10 significance level, can we conclude that less than 90 percent of the orders are delivered in less than 10 minutes?

Research at the University of Toledo indicates that 50 percent of students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.

According to the local union president, the mean 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 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.

Rutter Nursery Company packages its pine bark mulch n 50-pound bags. From a long history, the production department reports that the distribution of the bag weights follows the normal distribution and the standard deviation of this process is 3 pounds per bag. At the end of each day, Jeff Rutter, the production manager, weighs 10 bags and computes the mean weight of the sample. Below are the weights of 10 bags from today's production. $$\begin{array}{|lllllllll|}\hline 45.6 & 47.7 & 47.6 & 46.3 & 46.2 & 47.4 & 49.2 & 55.8 & 47.5 & 48.5 \\\\\hline \end{array}$$ a. Can Mr. Rutter conclude that the mean weight of the bags is less than 50 pounds? Use the .01 significance level. b. In a brief report, tell why Mr. Rutter can use the \(z\) distribution as the test statistic. c. Compute the \(p\) -value.

A new weight-watching company, Weight Reducers International, advertises that those who join will lose, on the average, 10 pounds the first two weeks with a standard deviation of 2.8 pounds. A random sample of 50 people who joined the new weight reduction program revealed the mean loss to be 9 pounds. At the .05 level of significance, can we conclude that those joining Weight Reducers on average will lose less than 10 pounds? Determine the \(p\) -value.

Dole Pineapple, Inc., is concerned that the 16 -ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounces. The quality-control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the \(p\) -value.

A statewide real estate sales agency, Farm Associates, specializes in selling farm property in the state of Nebraska. Its records indicate that the mean selling time of farm property is 90 days. Because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days. A statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. At the . 10 significance level, has there been an increase in selling time?

NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is 2.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, Wisconsin, area revealed that the mean price was \(\$ 2.52\) per gallon and that the standard deviation was 0.05 per gallon. At the .05 significance level, can we conclude that the price of gasoline is higher in the Milwaukee area? Determine the p -value.

A recent article in The Wall Street Journal reported that the 30-year mortgage rate is now less than 6 percent. A sample of eight small banks in the Midwest revealed the following 30-year rates (in percent): $$\begin{array}{|llllllll|}\hline 4.8 & 5.3 & 6.5 & 4.8 & 6.1 & 5.8 & 6.2 & 5.6 \\\\\hline\end{array}$$ At the .01 significance level, can we conclude that the 30 -year mortgage rate for small banks is less than 6 percent? Estimate the \(p\) -value.

According to the Coffee Research Organization (http://www.coffeeresearch.org) 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. $$\begin{array}{|llllllllllll|}\hline 3.1 & 3.3 & 3.5 & 2.6 & 2.6 & 4.3 & 4.4 & 3.8 & 3.1 & 4.1 & 3.1 & 3.2 \\\\\hline\end{array}$$ At the .05 significance level does this sample data suggest there is a difference between the national average and the sample mean from senior citizens?

The postanesthesia care area (recovery room) at St. Luke's Hospital in Maumee, Ohio, was recently enlarged The hope was that with the enlargement the mean number of patients per day would be more than \(25 .\) A random sample of 15 days revealed the following numbers of patients $$\begin{array}{|lllllllllllllll|}\hline 25 & 27 & 25 & 26 & 25 & 28 & 28 & 27 & 24 & 26 & 25 & 29 & 25 & 27 & 24 \\\\\hline\end{array}$$ At the .01 significance level, can we conclude that the mean number of patients per day is more than \(25 ?\) Estimate the \(p\) value and interpret it.

eGolf.com receives an average of 6.5 returns per day from online shoppers. For a sample of 12 days, it received the following number of returns $$\begin{array}{|llllllllllll|}\hline 0 & 4 & 3 & 4 & 9 & 4 & 5 & 9 & 1 & 6 & 7 & 10 \\\\\hline\end{array}$$ At the .01 significance level, can we conclude the mean number of returns is less than \(6.5 ?\)

During recent seasons, Major League Baseball has been criticized for the length of the games. A report indicated that the average game lasts 3 hours and 30 minutes. A sample of 17 games revealed the following times to completion. (Note that the minutes have been changed to fractions of hours, so that a game that lasted 2 hours and 24 minutes is reported at 2.40 hours.) Can we conclude that the mean time for a game is less than 3.50 hours? Use the .05 significance level. $$\begin{array}{|lllllllll|}\hline 2.98 & 2.40 & 2.70 & 2.25 & 3.23 & 3.17 & 2.93 & 3.18 & 2.80 \\\2.38 & 3.75 & 3.20 & 3.27 & 2.52 & 2.58 & 4.45 & 2.45 & \\\\\hline\end{array}$$

Watch Corporation of Switzerland claims that its watches on average will neither gain nor lose time during a week. A sample of 18 watches provided the following gains (+)or losses(-)in seconds per week. $$ \begin{array}{|rrrrrrrrr|}\hline-0.38 & -0.20 & -0.38 & -0.32 & +0.32 & -0.23 & +0.30 & +0.25 & -0.10 \\\\-0.37 & -0.61 & -0.48 & -0.47 & -0.64 & -0.04 & -0.20 & -0.68 & +0.05 \\\\\hline\end{array}$$ Is it reasonable to conclude that the mean gain or loss in time for the watches is \(0 ?\) Use the .05 significance level. Estimate the \(p\) -value.

Listed below is the rate of return for one year (reported in percent) for a sample of 12 mutual funds that are classified as taxable money market funds $$\begin{array}{|lllllllllll|}\hline 4.63 & 4.15 & 4.76 & 4.70 & 4.65 & 4.52 & 4.70 & 5.06 & 4.42 & 4.51 & 4.24 & 4.52 \\\\\hline\end{array}$$ Using the .05 significance level is it reasonable to conclude that the mean rate of return is more than 4.50 percent?

The publisher of Celebrity Living claims that the mean sales for personality magazines that feature people such as Angelina Jolie or Paris Hilton are 1.5 million copies per week. A sample of 10 comparable titles shows a mean weekly sales last week of 1.3 million copies with a standard deviation of 0.9 million copies. Does this data contradict the publisher's claim? Use the 0.01 significance level.

A United Nations report shows the mean family income for Mexican migrants to the United States is 27,000$ per year. A FLOC (Farm Labor Organizing Committee) evaluation of 25 Mexican family units reveals a mean to be 30,000 with a sample standard deviation of 10,000 . Does this information disagree with the United Nations report? Apply the 0.01 significance level.

Traditionally, two percent of the citizens of the United States live in a foreign country because they are disenchanted with U.S. politics or social attitudes. In order to test if this proportion has increased since the September 11, 2001, terror attacks, U.S. consulates contacted a random sample of 400 of these expatriates. The sample yields 12 people who report they are living overseas because of political or social attitudes. Can you conclude this data shows the proportion of politically motivated expatriates has increased? Use the 0.05 significance level.

According to a study by the American Pet Food Dealers Association, 63 percent of U.S. households own pets. A report is being prepared for an editorial in the San Francisco Chronicle. As a part of the editorial a random sample of 300 households showed 210 own pets. Does this data disagree with the Pet Food Dealers Association data? Use a .05 level of significance.

Tina Dennis is the comptroller for Meek Industries. She believes that the current cash-flow problem at Meek is due to the slow collection of accounts receivable. She believes that more than 60 percent of the accounts are in arrears more than three months. A random sample of 200 accounts showed that 140 were more than three months old. At the .01 significance level, can she conclude that more than 60 percent of the accounts are in arrears for more than three months? \(?\)

The policy of the Suburban Transit Authority is to add a bus route if more than 55 percent of the potential commuters indicate they would use the particular route. A sample of 70 commuters revealed that 42 would use a proposed route from Bowman Park to the downtown area. Does the Bowman-to- downtown route meet the STA criterion? Use the .05 significance level.

From past experience a television manufacturer found that 10 percent or less of its sets needed repair in the first two years of operation. In a sample of 50 sets manufactured two years ago, 9 needed repair. At the .05 significance level, has the percent of sets needing repair increased? Determine the \(p\) -value.

An urban planner claims that, nationally, 20 percent of all families renting condominiums move during a given year. A random sample of 200 families renting condominiums in the Dallas Metroplex revealed that 56 had moved during the past year. At the .01 significance level, does this evidence suggest that a larger proportion of condominium owners moved in the Dallas area? Determine the \(p\) -value.

The cost of weddings in the United States has skyrocketed in recent years. As a result many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised in Bride Magazine that the cost of a Caribbean wedding was less than \(\$ 10,000 .\) Listed below is a total cost in thousands of dollars for a sample of 8 Caribbean weddings $$\begin{array}{|llllllll|}\hline 9.7 & 9.4 & 11.7 & 9.0 & 9.1 & 10.5 & 9.1 & 9.8 \\\\\hline\end{array}$$ At the .05 significance level is it reasonable to conclude the mean wedding cost is less than \(\$ 10,000\) as advertised?

An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is 5,000. After introducing several plans to prevent loss, it randomly samples 200 policyholders and finds the mean amount per claim was 4,800 with a standard deviation of 1,300 . Does it appear the prevention plans were effective in reducing the mean amount of a claim? Use the .05 significance level.

A national grocer's magazine reports the typical shopper spends eight minutes in line waiting to check out. A sample of 24 shoppers at the local Farmer Jack's showed a mean of 7.5 minutes with a standard deviation of 3.2 minutes. Is the waiting time at the local Farmer Jack's less than that reported in the national magazine? Use the .05 significance level.

The Gallup Organization in Princeton, New Jersey, is one of the best-known polling organizations in the United States. It often combines with USA Today or CNN to conduct polls of current interest. It also maintains a website at: http://www.gallup.com/. Consult this website to find the most recent polling results on presidential approval ratings. You may need to click on Gallup Poll. Test whether the majority (more than 50 percent) approve of the president's performance. If the article does not report the number of respondents included in the survey, assume that it is \(1,000,\) a number that is typically used.