Problem 26
Sale Prices for Houses The average sales price of new one-family houses in the Midwest is dollar 250,000 and in the South is dollar 253,400. A random sample of 40 houses in each region was examined with the following results. At the 0.05 level of significance, can it be concluded that the difference in mean sales price for the two regions is greater than dollar 3400 ? $$ \begin{array}{lcc}{} & {\text { South }} & {\text { Midwest }} \\ \hline \text { Sample size } & {40} & {40} \\ {\text { Sample mean }} & {\$ 261,500} & {\$ 248,200} \\ {\text { Population standard deviation }} & {\$ 10,500} & {\$ 12,000}\end{array} $$
Problem 27
Average Earnings for College Graduates The average earnings of year-round full-time workers with bachelor's degrees or more is dollar 88,641 for men and dollar 58,000 for women - a difference of slightly over dollar 30,000 a year. One hundred of each were randomly sampled, resulting in a sample mean of dollar 90,200 for men, and the population standard deviation is dollar 15,000 ; and a mean of dollar 57,800 for women, and the population standard deviation is dollar 12,800. At the 0.01 level of significance, can it be concluded that the difference in means is not dollar 30,000 ?
Problem 27
For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Bullying Bullying is a problem at any age but especially for students aged 12 to 18 . A study showed that \(7.2 \%\) of all students in this age bracket reported that bullied at school during the past six months with 6 th grade having the highest incidence at \(13.9 \%\) and 12 th grade the lowest at \(2.2 \%\). To see if there is a difference between public and private schools, 200 students were randomly selected from each. At the 0.05 level of significance, can a difference be concluded? $$ \begin{array}{ccc}{} & {\text { Private }} & {\text { Public }} \\ \hline \text { Sample size } & {200} & {200} \\ {\text { No. bullied }} & {13} & {16}\end{array} $$
Problem 28
If there is a significant difference between \(p_{1}\) and \(p_{2}\) and between \(p_{2}\) and \(p_{3},\) can you conclude that there is a significant difference between \(p_{1}\) and \(p_{3} ?\)
