Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music 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 Spotify 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 .05, test the hypothesis of no difference in the mean number of households picking either service.

Businesses, particularly those in the food preparation industry such as General Mills, Kellogg, and Betty Crocker regularly use coupons as a brand allegiance builder to stimulate their retailing. There is uneasiness that the users of paper coupons are different from the users of e-coupons. One survey recorded the age of each person who redeemed a coupon along with the type. The sample of 35 e-coupon users had a mean age of 33.6 years with a standard deviation of 10.9, while a similar sample of 25 traditional paper-coupon clippers had a mean age of 39.5 with a standard deviation of 4.8. Assume the population standard deviations are not the same. Using a significance level of 0.01, test the hypothesis of no difference in the mean ages of the two groups of coupon clients.

A consumer buying cooperative tested the effective heating area of 20 different electric space heaters with different wattages. Here are the results.

$$\begin{array}{|crr|rrr|} \hline \text { Heater } & \text { Wattage } & \text { Area } & \text { Heater } & \text { Wattage } & \text { Area } \\ 1 & 1,500 & 205 & 11 & 1,250 & 116 \\ 2 & 750 & 70 & 12 & 500 & 72 \\ 3 & 1,500 & 199 & 13 & 500 & 82 \\ 4 & 1,250 & 151 & 14 & 1,500 & 206 \\ 5 & 1,250 & 181 & 15 & 2,000 & 245 \\ 6 & 1,250 & 217 & 16 & 1,500 & 219 \\ 7 & 1,000 & 94 & 17 & 750 & 63 \\ 8 & 2,000 & 298 & 18 & 1,500 & 200 \\ 9 & 1,000 & 135 & 19 & 1,250 & 151 \\ 10 & 1,500 & 211 & 20 & 500 & 44 \\ \hline \end{array}$$

a. Compute the correlation between the wattage and heating area. Is there a direct or an indirect relationship? b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient is greater than zero. Use the .05 significance level. c. Develop the regression equation for effective heating based on wattage. d. What heating area corresponds with a 1,500-watt heater?

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?

The research department at the home office of New Hampshire Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three-year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident. At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period? Determine the p-value

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.

A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to Plan A is $57,000 with a standard deviation of$9,200. This distribution is positively skewed; the actual coefficient of skewness is 2.11. For a sample of 30 subscribers to Plan B, the mean income is $61,000 with a standard deviation of$7,100. The distribution of Plan B subscribers is also positively skewed, but not as severely. The coefficient of skewness is 1.54. At the .05 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? What is the p-value? Do the coefficients of skewness affect the results of the hypothesis test?Why?

A computer manufacturer offers a help line that purchasers can call for help 24 hours a day, 7 days a week. Clearing these calls for help in a timely fashion is important to the company’s image. After telling the caller that resolution of the problem is important, the caller is asked whether the issue is software or hardware related. The mean time it takes a technician to resolve a software issue is 18 minutes with a standard deviation of 4.2 minutes. This information was obtained from a sample of 35 monitored calls. For a study of 45 hardware issues, the mean time for the technician to resolve the problem was 15.5 minutes with a standard deviation of 3.9 minutes. This information was also obtained from monitored calls. At the .05 significance level, does it take longer to resolve software issues? What is the p-value?

The article “That’s Rich: More You Drink, More You Earn” (Calgary Herald, April 16, 2002) reported that there was a positive correlation between alcohol consumption and income. Is it reasonable to conclude that increasing alcohol consumption will increase income? Give at least two reasons or examples to support your answer.

Listed below are sorted weights (g) of a sample of M&M plain candies randomly selected from one bag. Use the range rule of thumb to estimate the value of the standard deviation of all 345 M&Ms in the bag. Compare the result to the standard deviation of 0.0366 g computed from all of the 345 M&Ms in the bag.

0.799 0.843 0.849 0.855 0.870 0.872 0.874 0.875 0.879 0.886

0.887 0.889 0.894 0.901 0.902 0.902 0.926 0.940 0.943 0.944

There are two Chevrolet dealers in Jamestown, New York. The mean monthly sales at Sharkey Chevy and Dave White Chevrolet are about the same. However, Tom Sharkey, the owner of Sharkey Chevy, believes his sales are more consistent. Following are the numbers of new cars sold at Sharkey in the last 7 months and for the last 8 months at Dave White. Do you agree with Mr. Sharkey? Use the .01 significance level.

$$\begin{array}{|lllllllll} \text { Sharkey } & 98 & 78 & 54 & 57 & 68 & 64 & 70 & \\ \text { Dave White } & 75 & 81 & 81 & 30 & 82 & 46 & 58 & 101 \end{array}$$

The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow the normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 311 days with a standard deviation of 12 days. Did the modification increase the mean life of the battery? (a) State the null hypothesis and the alternate hypothesis. (b) Show the decision rule graphically. Use the $.05$ significance level. (c) Compute the value of $t$. What is your decision regarding the null hypothesis? Briefly summarize your results.

Explain why the federal government funds national defense.

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?