# Statistics Questions

(Part 1) A random sample of 1000 voters are classified as to whether they are in a low, medium, or high income bracket and whether they favor a new tax reform. The observed frequencies are presented in the table. [see attachment]

What is the following probability? P(M'|A)

(Part 2) Indications are that the average age at which breast cancer is detected in women has been changing. In a study to compare the situation in Canada today with that of twenty years ago, independent random samples were obtained from federal government health records for each of 1978 and 1998 relating to women who had developed this disease. The following table summarizes the information collected about age at detection. [see attachment] In performing the statistical test suggested in this question, a standard error must be estimated.

What is the estimated value of the standard error?

(Problem Set E) The results for random samples of international matches played between Canadian curlers and curlers from other countries were obtained for both male and female curlers. The information collected is summarized in the following table. [see attachment] In estimating the difference in the proportions of games one by male and female curlers, the 99% confidence interval could be expressed as (pM - pF) +/- E.

In this case, the quantity denoted E would have what value?

See attached file for full problem description.

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#### Solution Preview

Part 1

What is...

This question means "what is the probability of the complement of M (not-M) occurring, given that A is true?" Assuming that M means medium income and A means against, the question should read "what is the probability that someone is not in the medium income bracket (i.e. they are in the low or high bracket) given that they are against the new property tax?"

We know from the table that there are 402 people against the tax, and 154 + 110 = 264 of those people are not in the medium income bracket. Therefore, the probability that someone is not in the medium income bracket ...

#### Solution Summary

The expert examines probability, standard errors and confidence intervals in statistics. Probability of a function is determined.