61) Housing costs A government report on housing costs says that single - family home prices nationwide are skewed to the right, with a mean of $235,700. We want to see how home prices in Orange County, California compare with those nationwide. a. We collect price data from a random sample of 50 homes in Orange County, California. Why is it okay to use these data for inference even though the population is skewed? b. The standard deviation of the 50 homes in our sample was $25,500. Specify the sampling model for the mean price of such samples. c. This sample of randomly chosen homes produced a 90%% confidence interval for the mean price in Orange County of ($233954, $246046). Does this interval provide evidence that single- family home prices are unusually high in this county? Explain briefly d. Suppose we want to collect a new sample. How many homes must we survey to have 90%% confidence of estimating the mean local price to within $2000? The average American sees 3.9 movies at the theater each year. A curious student polls 30 friends and family over the course of a week. He finds that his friends have seen an average of 45 movies with a standard deviation of 1.2 movies. 62) Does this sample provide evidence that people are attending the movies more often? Provide a complete significance test to support your answer. 63) The student insists to his media teacher at school that movie attendance is on the rise. Do you agree with this conclusion? 64) Find and interpret a 95%% confidence interval for this sample. In 2010, the United Nations claimed that there was a higher rate of illiteracy in men than in women from the country of Qatar. A humanitarian organization went to Qatar to conduct a random sample. The results revealed that 45 out of 234 men and 42 out of 251 women were classified as illiterate on the same measurement test. Do these results indicate that the United Nations findings were correct? 65) Test an appropriate hypothesis and state your conclusion. 66) Find a 95%% confidence level for the difference in the proportions of illiteracy in men and women from Qatar. Interpret your interval