Hi Jenny,

Here is some help for you.

1. This one is only an application of the formula for confidence intervals: the margin of error is given by , where is such that for a standard normal random variable , i.e. (you may be used to another notation for this quantity). Just replace and by their values in the formula and take your calculator.

2. Here are steps: First find the test the question is about. This amounts to finding a 95% confidence interval for the proportion of females among 20 people, males and females being equally likely. Then look for the probability that the proportion of females falls outside this interval (i.e. the test tells "H0 is false"), in the case when the probability of a female is no more 0.5 but 0.7 (you can approximate the proportion of women by a normal random variable of mean 0.7 and stdd deviation ). This reduces to looking up in tables quantities like where is a standard Gaussian random variable. I leave it to you to precise all this...

I hope this helped you,

Laurent.