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# Probability and P-Values

See the attached file.
There are two boxes, Box A and Box B. Box A has 40 tags with the number 1, 50 tags with the number 10, and 10 tags with the number 100. Box B has 40 tags with the number 100, 50 tags with the number 10, and 10 tags with the number 1. A box is picked at random and exactly one tag is drawn at random from that box. You do not know if the box picked was Box A or Box B.

a) State the null and alternative hypotheses.

c) If the decision rule is to reject Ho if a tag value of 100 is obtained, what is the significance level? What does the significance level represent?

d) What is the numerical value of ß (beta). What does ß represent?

e) If the tag drawn is 10, what is the numerical value of the p-value. What is your decision?

#### Solution Preview

See the attached file.
Question 1:

There are two boxes, Box A and Box B. Box A has 40 tags with the number 1, 50 tags with the number 10, and 10 tags with the number 100. Box B has 40 tags with the number 100, 50 tags with the number 10, and 10 tags with the number 1. A box is picked at random and exactly one tag is drawn at random from that box. You do not know if the box picked was Box A or Box B.

First, I'm going to make a table of the frequencies, so that the data is easier to understand.

Box A Box ...

#### Solution Summary

The solution determines the probability and p-values.

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