20.The following is a partial ANOVA table:

1. How many treatments are there?
2. What is the total sample size?
3. What is the critical value of F?
4. Write out the null and alternate hypotheses.
5. What is your conclusion regarding the null hypothesis?

26. There are four auto body shops in Bangor, Maine, and all claim to promptly serve customers. To check if there is any difference in service, customers are randomly selected from each repair shop and their waiting times in days are recorded. The output from a statistical software package is:

Summary

ANOVA

Is there evidence to suggest a difference in the mean waiting times at the four body shops? Use the .05 significance level.

28. Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of six hourly periods is chosen for each assembly line and the number of components produced during these periods for each line is recorded. The output from a statistical software package is:

Summary

ANOVA

1. Use a .01 level of significance to test is there is a difference in the mean production of the three assembly lines.
2. Develop a 99 percent confidence interval for the difference in the means between line B and Line C.

38. A suburban hotel derives its gross income from its hotel and restaurant operations. The owners are interested in the relationship between the number of rooms occupied on a nightly basis and the revenue per day in the restaurant. Below is a sample of 25 days (Monday through Thursday) from last year showing the restaurant income and number of rooms occupied?

Use a statistical software package to answer the following questions.

1. Does the breakfast revenue seem to increase as the number of occupied rooms’ increases? Draw a scatter diagram to support your conclusion.
2. Determine the coefficient of correlation between the two variables. Interpret the value.
3. Is it reasonable to conclude that there is a positive relationship between revenue and occupied rooms? Use the .10 significance level.
4. What percent of the variation in revenue in the restaurant is accounted for by the number of rooms occupied?

52. The following table shows the mean annual percent return on capital (profitability) and the mean annual percentage sales growth for eight aerospace and defense companies.

1. Compute the coefficient of correlation. Conduct a test of hypothesis to determine if it is reasonable to conclude that the population correlation is greater than zero. Use the .05 significance level.
2. Develop the regression equation for profitability based on growth. Comment on the slope value.
3. Use a software package to determine the residual for each observation. Which company has the largest residual?

Solution: (a) We get

The correlation is r = -0.059, and the two-tailed p-value is p = 0.890, which means that the correlation is not significantly positive.

(b) We get the following regression results:

The model is

Profitability = 17.932 – 0.032*Growth

The slope value is negative, but in fact, this value is not significantly different from zero.

(c) The residuals are:

Hence, the largest residual corresponds to Rockwell Collins.

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