Based on information from the National Center for Health Statistics, the heights of 10-year-old girls closely follow a Normal distribution with mean 54.5 inches and standard deviation 2.7 inches. The heights of 10-year-old boys follow a Normal distribution with mean 54.1 inches and standard deviation 2.4 inches. A particular fourth-grade class has 10 girls and 7 boys. The children's heights are recorded on their tenth birthdays. (a) Treat the students in this class as random samples of 10-year-old boys and girls. Use random variables to calculate the probability that the mean height of the girls is greater than the mean height of the boys. Show your work.

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10