# Histograms and Probabilities

Manufacturing plants A and B produce sports shoes.

The following are the data for plant A:

39, 32, 34, 40, 45, 35, 54, 36, 40, 41, 55, 43, 44, 46, 47, 49, 51, 54, 59, 46

The following are the data for Plant B:

27, 37, 29, 44, 31, 33, 34, 46, 58, 59, 32, 32, 55, 57, 63, 33, 56, 58, 62, 51

a) Make a histogram, one above the other for each of the Plants. For Plant A use a lower limit of 20, an upper limit of 65, and class width of 5. For Plant B use a lower limit of 20, and upper limit of 65, and a class width=5.

b) Describe the shape of each histogram.

c) An unknown shoe (that is, it is not known whether it was produced at plant A or Plant B) has a price tag of $55. We wish to test the following hypotheses:

Ho: The unknown shoe comes from Plant A.

H1: The known shoe comes from Plant B.

d) What is the direction of extreme?

e) Using the histogram, find the p-value corresponding to the observed value of $55.

f) What is the decision at a = 0.15?

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Question 2:

Manufacturing plants A and B produce sports shoes.

The following are the data for plant A:

39, 32, 34, 40, 45, 35, 54, 36, 40, 41, 55, 43, 44, 46, 47, 49, 51, 54, 59, 46

The following are the data for Plant B:

27, 37, 29, 44, 31, 33, 34, 46, 58, 59, 32, 32, 55, 57, 63, 33, 56, 58, 62, 51

a) Make a histogram, one above the other for each of the Plants. For Plant A use a lower limit of 20, an upper limit of 65, and class width of 5. For Plant B use a lower limit of 20, and upper limit of 65, and a class width=5.

First, you have to figure out the frequencies for each ...

#### Solution Summary

This problem set involves making histograms from a given data set. The solution contains solutions and explanations to parts a - c and e - f. A Word document and an Excel spreadsheet are attached.