Determine the degrees of freedom and the corresponding critical value, and rejection and non-rejection regions.
1. (25 points) A survey of 220 ninth-graders found that 33.5% had used cigarettes in the past week and a survey of 240 high-school seniors found that 36.4% had used cigarettes in the past week. Is there significant difference between the two corresponding population proportions?
(a) State the hypotheses.
(b) Using a 5% significance level, determine the rejection and non-rejection regions.
(c) Calculate the test statistic and the p-value, and interpret the results, and answer the original question.
(d) Calculate the 95% confidence interval for the difference between the two population proportions. How does this result relate to the results in part (c)?
2. (25 points) A sample of 65 male professors at a major four-year university produced a mean annual pay of $74,800 and a standard deviation of $4,850. A sample of 60 female professors at the same university produced a mean annual pay of $70,250 and a standard deviation of $5,250. Does this constitute enough evidence to conclude that male and female professors at this university are not paid the same?
(a) State the hypotheses.
(b) Using a 5% significance level, determine the rejection and non-rejection regions.
(c) Calculate the test statistic and the p-value, and interpret the results, and answer the original question.
(d) Calculate the 95% confidence interval for the difference between the two population means. How does this result relate to your conclusions in part (c)?
3. (25 points) Consider the following result of a one-way ANOVA performed on different groups of textbooks at a local college bookstore. Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
BIOLOGY 803.19 100.39875 1342.369
MATHEMATICS 847.74 94.1933333 575.72903
SOCIOLOGY 680.34 97.1914286 1107.536
ANOVA
Source of Variation SS df MS F P-value
Between Groups 163.119389 2 81.5596946 0.0829516 0.92069577
Within Groups 20647.6314 21 983.220542
Total 20810.7508 23
(a) State the null and alternative hypotheses.
(b) Determine the degrees of freedom and the corresponding critical value, and rejection and non-rejection regions.
(c) Determine the total number of data values in these three samples.
(d) Identify the p-value, and interpret the result (in other words, answer whether there is a significant difference between the average price of textbooks in the three groups).
4. (25 points) Consider the Salt-Blood Pressure Data set available in Data Sets in Excel in the main menu. Here, let the amount of salt (sodium) be the predictor (independent) variable, and the blood pressure be the response (dependent) variable. You would like to examine the relationship between the salt intake and blood pressure.
(a) Display the scatter plot of the data.
(b) Display all the relevant regression results. Identify the slope and the y-intercept, and write the regression equation.
(c) Using the regression line, find the blood pressure for a person whose salt intake is at 5.5.
(d) Identify the coefficient of determination, and interpret the result.