t has been reported that the average life for halogen lightbulbs is 4000 hours. Learning of this figure, a plant manager would like to find out whether the vibration and temperature conditions that the facility's bulbs encounter might be having an adverse effect on the service life of bulbs in her plant. In a test involving 15 halogen bulbs installed in various locations around the plant, she finds the average life for bulbs in the sample is 3882 hours, with a standard deviation of 200 hours. Assuming the population of halogen bulb lifetimes to be approximately normally distributed, and using the $0.025$ level of significance, do the test results tend to support the manager's suspicion that adverse conditions might be detrimental to the operating lifespan of halogen lightbulbs used in her plant?

A manager wants to assign tasks to workstations as efficiently as possible and achieve an hourly output of 33 1/3 units. Assume the shop works a 60-minute hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. In order of most following tasks. Tiebreaker: greatest positional weight. b. In order of greatest positional weight. Tiebreaker: most following tasks. c. What is the efficiency?

Using the sample results in Exercise 10.49, construct and interpret the $95 \%$ confidence interval for the population mean. Is the hypothesized population mean $(\$ 640,000)$ within the interval? Given the presence or absence of the $\$ 640,000$ value within the interval, is this consistent with the findings of the hypothesis test conducted in Exercise 10.49?

On CNN and other news networks, guests often express their opinions in rather strong, persuasive, and sometimes frightening terms. For example, a scientist who strongly believes that global warming is taking place will warn us of the dire consequences (such as rising sea levels, coastal flooding, and global climate change) she foresees if we do not take her arguments seriously. If the scientist is correct, and the world does not take her seriously, would this be a Type I error or a Type II error? Briefly explain your reasoning.

A manager wants to assign tasks to workstations as efficiently as possible and achieve an hourly output of four units. The department uses a working time of 56 minutes per hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules: a. In order of most following tasks. Tiebreaker: greatest positional weight. b. In order of greatest positional weight. Tiebreaker: most following tasks. c. What is the efficiency?

According to the Federal Reserve Board, the mean net worth of U.S. households headed by persons 75 years or older is $\$ 640,000$. Suppose a simple random sample of 50 households in this age group is obtained from a certain region of the United States and is found to have a mean net worth of $\$ 615,000$, with a standard deviation of $\$ 120,000$. From these sample results, and using the $0.05$ level of significance in a two-tail test, comment on whether the mean net worth for all the region's households in this age category might not be the same as the mean value reported for their counterparts across the nation.

Planetary Communications, Inc., intends to launch a satellite that will enhance reception of television programs in Alaska. According to its designers, the satellite will have an expected life of six years. Assume the exponential distribution applies. Determine the probability that it will function for each of the following time periods:

a. More than 9 years.

b. Less than 12 years.

c. More than 9 years but less than 12 years.

d. At least 21 years

A scrap metal dealer claims that the mean of his cash sales is "no more than $\$ 80$," but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchase to be $\$ 91$, with a standard deviation of $\$ 21$. Assuming the population is approximately normally distributed, and using the $0.05$ level of significance, is the agent's suspicion confirmed?

During 2008 , college work-study students earned a mean of $\$ 1478$. Assume that a sample consisting of 45 of the work-study students at a large university was found to have earned a mean of $\$ 1503$ during that year, with a standard deviation of $\$ 210$. Would a one-tail test at the $0.05$ level suggest the average earnings of this university's work-study students were significantly higher than the national mean? Source: Bureau of the Census, Statistical Abstract of the United States 2009, p. 178, .m.

The new director of a local YMCA has been told by his predecessors that the average member has belonged for $8.7$ years. Examining a random sample of 15 membership files, he finds the mean length of membership to be $7.2$ years, with a standard deviation of $2.5$ years. Assuming the population is approximately normally distributed, and using the $0.05$ level, does this result suggest that the actual mean length of membership may be some value other than $8.7$ years?

Taxco, a firm specializing in the preparation of income tax returns, claims the mean refund for customers who received refunds last year was $\$ 150$. For a random sample of 12 customers who received refunds last year, the mean amount was found to be $\$ 125$, with a standard deviation of $\$ 43$. Assuming that the population is approximately normally distributed, and using the $0.10$ level in a two-tail test, do these results suggest that Taxco's assertion may be accurate?

The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as $1.65$ cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of $1.84$ cups of coffee per day, with a standard deviation of $0.85$ cups. In a two-tail test at the $0.05$ level, could the residents of this city be said to be significantly different from their counterparts across the nation?

For a simple random sample of 15 items from a population that is approximately normally distributed, $\bar{x}=82.0$ and $s=20.5$. At the $0.05$ level of significance, test $H_0: \mu \geq 90.0$ versus $H_1: \mu<90.0$.

The average length of a flight by regional airlines in the United States has been reported as 464 miles. If a simple random sample of 30 flights by regional airlines were to have $\bar{x}=479.6$ miles and $s=42.8$ miles, would this tend to cast doubt on the reported average of 464 miles? Use a two-tail test and the $0.05$ level of significance in arriving at your answer.