The proprietor of Bun 'N' Run Hamburgers wants to contrast the day sales at two different establishments. At the Northside site, the mean number sold over the course of ten days was 83.55, with a standard deviation of 10.50. The average number of sales for a random 12-day period at the Southside site was 78.80, with a standard deviation of 14.25. Is there a difference in the mean number of hamburgers sold at the two places at the.05 level of significance? What does p-value mean?

A coffee manufacturer is interested in whether the mean daily consumption of regular-coffee drinkers is less than that of decaffeinated-coffee drinkers. Assume the population standard deviation for those drinking regular coffee is 1.20 cups per day and 1.36 cups per day for those drinking decaffeinated coffee. A random sample of 50 regular-coffee drinkers showed a mean of 4.35 cups per day. A sample of 40 decaffeinated-coffee drinkers showed a mean of 5.84 cups per day. Use the .01 significance level. Compute the p-value.

You are researching the hypothesis that there is no difference in the percentage of public school students who smoke and the percentage of private school students who smoke. You find these results from a recent survey.

Based on these figures, reply to the given question:

6. If so, complete the test and summarize the results.

What is your opinion of musicians licensing their music to advertisements? Is this "selling out" or is it a smart way for a win-win for marketers and musicians?

One of the music industry’s most pressing questions is: Can paid download stores contend nose-to-nose with free peer-to-peer download services? Data gathered over the last 12 months show Apple’s iTunes was used by an average of 1.65 million households with a sample standard deviation of 0.56 million family units. Over the same 12 months WinMX was used by an average of 2.2 million families with a sample standard deviation of 0.30 million. Assume the population standard deviations are not the same. Using a significance level of 0.05, test the hypothesis of no difference in the mean number of households picking either variety of service to download songs.

The null and alternate hypotheses are:

$$H_0:μ_1≤μ_2; H_1:μ_1>μ_2$$

A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. Use the .05 significant level.

Streaming music services have changed the way we listen to music. Spotify, Pandora, Tidal, and Google Play are some of the more popular services. These companies offer free access to music. For a small monthly fee users can purchase premium access and listen to millions of songs on demand and ad free. But not all artists are fans of free streaming music. In 2016 , Taylor Swift's move to prevent Spotify from playing her new release, 1989 , for free, made national headlines. When Spotify refused to restrict access to only paying customers, Swift would not allow the company to play her music for free. She is not alone. Adele, Dr. Dre, Garth Brooks, and Coldplay have all had runins with free streaming services.

a. If music lovers obtain music and video content via free music streaming services, instead of buying it directly or paying for premium access, what would the record companies' producer surplus be from music sales? What are the implications for record companies' incentive to produce music content in the future?

b. If Taylor Swift and other artists were not allowed to pull their music from the free streaming services, what would happen to mutually beneficial transactions (the producing and buying of music) in the future?

Explain why the federal government funds national defense.

Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.

$$\begin{array}{|llllllll|} \hline \text{ Sales (\$) } & 131 & 135 & 146 & 165 & 136 & 142 & \\ \text{ Audit (\$) } & 130 & 102 & 129 & 143 & 149 & 120 & 139 \\ \hline \end{array}$$

Can she draw the conclusion that the mean daily expenses for the audit personnel are lower than for the sales staff at the.10 significance level? What does p-value mean?

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.

Gibbs Baby Food Company wishes to compare the weight gain of infants using its brand versus its competitor’s. A sample of 40 babies using the Gibbs products revealed a mean weight gain of 7.6 pounds in the first three months after birth. For the Gibbs brand, the population standard deviation of the sample is 2.3 pounds. A sample of 55 babies using the competitor’s brand revealed a mean increase in weight of 8.1 pounds. The population standard deviation is 2.9 pounds. At the .05 significance level, can we conclude that babies using the Gibbs brand gained less weight? Compute the p-value and interpret it.

A sample of 36 observations is selected from a normal population. The sample mean is 12 , and the population standard deviation is 3 . Conduct the following test of hypothesis using the 01 significance level.

$$\begin{aligned} & H_0: \mu \leq 10 \\ & H_1: \mu>10 \end{aligned}$$

A population is estimated to have a standard deviation of 10. We want to estimate the population mean within 2, with a 95 percent level of confidence. How large a sample is required?

What is the interpretation of a 96% confidence level?