1.A study of 500 randomly selected homes found 11that were vacant. Does this suggest that the home vacancy rate is different than its previous value of 2.5%?

2.A 2009 study suggested that 13% of new mothers will experience postnatal depression. A doctor wants to determine if this value has lowered with better medical training in the past few years, and he plans to conduct a test at the 10% level of significance.

a. What range of z statistics will lead him to reject H₀: p=0.13 in favor of H_a: p<0.13? Assume the doctor runs a study with 100 participants.

b. What is the maximum number out of 10 who can report experiencing postnatal depression that would still lead to the doctor concluding that the rate of depression has decreased at the 10% significance level?

3.The International Olympic Committee states that the female participation in the 2004 Summer Olympic Games was 42%, even with new sports such as weight lifting, hammer throw, and modern pentathlon being added to the Games. Broadcasting and clothing companies want to change their advertising and marketing strategies if the female participation increases at the next games. An independent sports expert arranged for a random sample of pre-Olympic exhibitions. The sports expert reported that 202 of 454 athletes in the random sample were women. Is this strong evidence that the participation rate may increase?