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Chapter 10, exercise number 18

18. The management of White Industries is considering a new method of assembling its golf cart. The present method requires 42.3 minutes, on the average, to assemble a cart. The mean assembly time for a random sample of 24 carts, using the new method, was 40.6 minutes, and the standard deviation of the sample was 2.7 minutes. Using the .10 level of significance, can we conclude that the assembly time using the new method is faster?

A. Analysis of variance (ANOVA) is used to determine if there is a difference between the means of different populations. For example, I had a student in Prescott who raised hens. A company was trying to sell her the feed they produced by claiming that if her hens ate their feed the hens would produce more eggs. They offered her a study to read in which they demonstrated that their feed was the best. To support this they conducted an experiment in which they fed four different types of food, including their own, to groups of hens. They wanted to show that on average hens that ate their food produced more eggs. They used analysis of variance. This is a true story. Can you think of examples at work in which ANOVA is used or could be used?

B. The personnel manager of a large finance company wished to evaluate the effectiveness of 4 different sales-training programs designed for new employees. A group of 32 recently hired employees are randomly assigned to the 4 training programs so that there are 8 subjects in each program. At the end of the program an exam is given and the scores are as follows;

66 72 61 63
74 51 60 61
82 59 57 76
75 62 60 84
73 74 81 58
97 64 55 65
87 78 70 69
78 63 71 80

C. At a five percent significance level, use the one-way ANOVA to determine if there is evidence of a significant difference in the fore training programs?

D. Suggest applications of nonparametric methods to solving business related problems. Describe the example. How are you or could you use nonparametric methods to solve business related problems?

E. Surveys are used to facilitate marketing efforts by assessing both potential customers' evaluations of products and the characteristics of the same customers. In other words, surveys provide the data necessary to use the chi-square distribution to test hypotheses related to whether or not a statistically significant relationship exists between the characteristics of customers and their evaluation of products. With this in mind, propose survey questions to evaluate customers' preferences for a good or service you are familiar with and also questions designed to identify the characteristics of these customers.

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Solution Summary

This provides examples of a series of statistics questions, including designing appropriate questions, nonparametric methods, one-way ANOVA, and level of significance.

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Sufficiency and Order Statistics

Let Y1<Y2<...<Yn be the order statistics of a random sample of size n from the uniform distribution over the closed interval [-theta, theta ]
having pdf f(x; theta ) = (1/2(theta))I[-theta , theta ](x).

Argue that the mle of theta; equals theta;hat= max(-Y1, Yn).
Demonstrate that the mle theta;hat is a sufficient statistic for theta;.
Define at least two ancillary statistics for this distribution

See attachment for better symbol representation.

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