1.One of the most important aspects of a store’s image is the perceived quality of its merchandise. Other factors include merchandise pricing, assortment of products, convenience of location, and service. Suppose image perceptions of shoppers of specialty stores and shoppers of discount stores are being compared. A random sample of shoppers is taken at each type of store, and the shoppers are asked whether the quality of merchandise is a determining factor in their perception of the store’s image. Out of 350 shoppers at the specialty store, 210 say yes; but only 260 of the 500 shoppers at the discount store say yes. Use these data to test to determine if there is a significant difference between the proportion of shoppers at specialty stores and the proportion of shoppers at discount stores who say that quality of merchandise is a determining factor in their perception of a store’s image.

a.Formulate the null and alternative hypotheses.

b.Using a 10% level of significance, test to determine if there is a significant difference between the proportion of shoppers at specialty stores and the proportion of shoppers at discount stores who say that quality of merchandise is a determining factor in their perception of a store’s image. Find *p*-value. Write conclusion.

2,Is the variation in the output of one shift in a manufacturing plant same as in another shift? In an effort to study this question, plant managers gathered productivity reports from the 8 A.M. to 4 P.M. shift for eight days. The reports indicated that the following numbers of units were produced on each day for this shift.

5528 |
4779 |
5112 |
5380 |

4918 |
4763 |
5055 |
5106 |

Productivity information was also gathered from seven days for the 4 P.M. to midnight shift, resulting in the following data.

4325 |
4016 |
4872 |
4559 |

3982 |
4754 |
4116 |

Assume productivity is normally distributed in the population.

a.Formulate the null and alternative hypotheses.

b. Use above data and *a*= .01to test to determine whether the variances of productivity for the two shifts are the same. Place a box around *p*-value.

3. A company sells identical soap in three different packages at the same price. The sales of each package type for 12 months are listed in the file

a)Is there any indication of differences in the mean sales of this brand of soap across the various package types? Perform an appropriate statistical test and report a *p*-value.Use a= 0.05.

b)Use a= 0.05, and construct confidence intervals for all pairs of differences between means. Which of these differences, if any, are statistically significant at the selected significance level? Are you surprised with your findings?

4. Use**Part-4**sheet to answer this question.

The human resources manager of DataCom, Inc., wants to examine the relationship between annual salaries (*Y*) and the number of years employees have worked at DataCom (*X*). These data have been collected for a sample of employees and are given in the file

a)Create a scatterplot of the annual salaries (*Y*) versus the number of years employees have worked (*X*). Does it appear that the relationship is linear?

b)Estimate a simple linear regression equation using the given data and interpret it.

c)What is the value of R^2 this model? Explain R^ words.

d)Is this model statistically significant? What is the *p*-value? Use alpha=0.05.

e)Draw a normal probability plot of residuals by finding out the Z-score of the residuals. Use Excel. Plot Z-score at Y- axis and residuals at X -axis. Do the residuals seem normally distributed? Explain

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