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.

Coffee consumption in the United States is greater on a per capita basis than anywhere else in the world. However, due to price fluctuations of coffee beans and worries over the health effects of caffeine, coffee consumption has varied considerably over the years. According to data published in The Wall Street Journal, the number of cups f(x) consumed daily per adult in year x (with 1955 corresponding to x=0 ) is given by the mathematical model

$$f(x)=2.77+0.0848 x-0.00832 x^2+0.000144 x^3 .$$

(a) Graph y=f(x) to show daily coffee consumption from 1955 through 1994.

(b) Use $f^{\prime}(x)$ to determine the year in which coffee consumption was least during this period. What was the daily coffee consumption at that time?

(c) Use $f^{\prime}(x)$ to determine the year in which coffee consumption was greatest during this period. What was the daily coffee consumption at that time?

(d) Use $f^{\prime \prime}(x)$ to determine the year in which coffee consumption was decreasing at the greatest rate.

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.

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.

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?

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.

Industrial engineer Clark Heter works at Lyons Products. He wants to know if more units are created during the night shift than during the day shift. A sample of 54 day shift workers produced an average of 345 units. A survey of 60 night shift workers yielded a mean of 351, which is the number of units. Take into account that the population standard deviation of the quantity of units produced during the day shift is 21 and during the night shift is 28. Is the number of units produced during the night shift higher, using the.05 significance level?

The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of 10 customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58,$19.73, $12.61,$17.79, $16.22,$15.82, $15.40,$15.86, $11.82, and$15.85. A sample of 14 customers at the Plum Street store revealed they spent the following amounts more than they planned: $18.19,$20.22, $17.38,$17.96, $23.92,$15.87, $16.47,$15.96, $16.79,$16.74, $21.40,$20.57, $19.79, and$14.83. At the .01 significance level, is there a difference in the mean amounts purchased on impulse at the two stores?

A sample of 65 observations is selected from one population with a population standard deviation of 0.75. The sample mean is 2.67. A sample of 50 observations is selected from a second population with a population standard deviation of 0.66. The sample mean is 2.59. Conduct the following test of hypothesis using the .08 significance level.a. Is this a one-tailed or a two-tailed test? b. State the decision rule. c. Compute the value of the test statistic. d. What is your decision regarding H0? e. What is the pvalue?

$$H_0:μ_1≤μ_2; H_1:μ_1>μ_2$$

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?

A real estate agent in the coastal area of Georgia wants to compare the variation in the selling price of homes on the oceanfront with those one to three blocks from the ocean. A sample of 21 oceanfront homes sold within the last year revealed the standard deviation of the selling prices was $45,600. A sample of 18 homes, also sold within the last year, that were one to three blocks from the ocean revealed that the standard deviation was$21,330. At the .01 significance level, can we conclude that there is more variation in the selling prices of the oceanfront homes?

What seven functions does packaging now perform?

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?

Identify the sampling technique used, and discuss potential sources of bias (if any). Explain. Questioning students as they leave a university library, a researcher asks 358 students about their drinking habits.