Suppose it has previously been claimed that the proportion of adults in a certain city that have a university degree is 0.58, and suppose we wish to carry out a test of the null hypothesis that this is the true proportion. In a random sample of 800 adults in this city, 588 have a university degree. What is the value of the appropriate Z test statistic?

(Give your numeric response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols. If the value is negative, include the negative sign)

Suppose we are about to carry out 99 independent hypothesis tests. We intend to carry out each test at a significance level of 0.05. Suppose that the assumptions of each test are true, and, unknown to us, the null hypothesis is true in all 99 situations.

What is the probability that we make a Type I error in exactly 7 of the 99 tests?

(Give your numeric response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols.)