The heights of a population of mother-daughter pairs have a bivariate normal distribution with correlation 0.5. a) Of the mothers on the 90th percentile of mothers' heights, what proportion have daughters who are taller than the 90th percentile of daughters' heights? b) In what proportion of mother-daughter pairs are both women taller than average? (This means the mothers are taller than the average mother and the daughters are taller than the average daughter.) [Hint: Remember that you can express standard bivariate normal variables in terms of two independent standard normal variables.]

Listed in the accompanying table are heights (in.) of mothers and their first daughters. The data pairs are from a journal kept by Francis Galton. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.05 significance level to test the claim that there is no difference in heights between mothers and their first daughters. Mother 64.0 66.0 63.0 62.0 66.5 66.0 65.0 60.0 67.0 63.0 Daughter 67.0 66.5 70.5 66.0 61.0 66.0 65.5 65.0 67.0 65.0 In this example, Hd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the daughter's height minus the mother's height. What are the null and alternative hypotheses for the hypothesis test? Ho: Ha = 0 in. H₁ Hd 0 in. (Type integers or decimals. Do not round.) Identify the test statistic. t= (Round to two decimal places as needed.)

Which of the following is NOT a requirement of testing a claim about the mean of the differences from dependent samples? Choose the correct answer below. O A. The degrees of freedom aren- 2. O B. The samples are simple random samples. O C. The sample data are dependent. O D. Either the number of pairs of sample data is larger than 30 or the pairs have differences that are from a population having a distribution that is approximately normal, or both.

1. For a normal distribution, find the percent of scores that lie between the scores having z values of z = -4 and z = 6