Question

A sociologist is interested in the relation between x = number of job changes and y = annual salary (in thousands of dollars) for people living in the Nashville area. A random sample of 10 people employed in Nashville provided the following information. x (number of job changes) 5 4 3 6 1 5 9 10 10 3 y (Salary in $1000) 34 32 37 32 32 38 43 37 40 33 A button hyperlink to the SALT program that reads: Use SALT. In this setting we have Σx = 56, Σy = 358, Σx2 = 402, Σy2 = 12,948, and Σxy = 2079. (a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to four decimal places.) x = 5.6 Correct: Your answer is correct. y = 35.8 Correct: Your answer is correct. b = .8394 Correct: Your answer is correct. ŷ = 31.0995 Correct: Your answer is correct. + .8394 Correct: Your answer is correct. x (b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y). WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Correct: Your answer is correct. (c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.) r = .688 Correct: Your answer is correct. r2 = .473 Correct: Your answer is correct. What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.) 47.3 Correct: Your answer is correct. % (d) Test the claim that the population correlation coefficient ρ is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = 1.833 Incorrect: Your answer is incorrect. Find or estimate the P-value of the test statistic. P-value > 0.250 0.125 < P-value < 0.250 0.100 < P-value < 0.125 0.075 < P-value < 0.100 0.050 < P-value < 0.075 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 0.0005 < P-value < 0.005 P-value < 0.0005 Incorrect: Your answer is incorrect. Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0. Reject the null hypothesis. There is insufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is sufficient evidence that ρ > 0. Fail to reject the null hypothesis. There is insufficient evidence that ρ > 0. Incorrect: Your answer is incorrect. (e) If someone had x = 7 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.) thousand dollars (f) Find Se. (Round your answer to three decimal places.) Se = 2.942 Correct: Your answer is correct. (g) Find a 90% confidence interval for the annual salary of an individual with x = 7 job changes. (Round your answers to two decimal places.) lower limit thousand dollars upper limit thousand dollars (h) Test the claim that the slope β of the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = Find or estimate the P-value of the test statistic. P-value > 0.250 0.125 < P-value < 0.250 0.100 < P-value < 0.125 0.075 < P-value < 0.100 0.050 < P-value < 0.075 0.025 < P-value < 0.050 0.010 < P-value < 0.025 0.005 < P-value < 0.010 0.0005 < P-value < 0.005 P-value < 0.0005 Conclusion Reject the null hypothesis. There is sufficient evidence that β > 0. Reject the null hypothesis. There is insufficient evidence that β > 0. Fail to reject the null hypothesis. There is sufficient evidence that β > 0. Fail to reject the null hypothesis. There is insufficient evidence that β > 0. (i) Find a 90% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.) lower limit upper limit Interpretation For each additional job change, the annual salary increases by an amount that falls within the confidence interval. For each additional job change, the annual salary increases by an amount that falls outside the confidence interval. For each less job change, the annual salary increases by an amount that falls within the confidence interval. For each less job change, the annual salary increases by an amount that falls outside the confidence interval.

Answer 1

(d) Test the claim that the population correlation coefficient ρ is positive at the 5% level of significance. (Round your test statistic to three decimal places.) t = 2.681

Find or estimate the P-value of the test statistic.

0.010 < P-value < 0.025

Conclusion Reject the null hypothesis. There is sufficient evidence that ρ > 0.

(e) If someone had x = 7 job changes, what does the least-squares line predict for y, the annual salary? (Round your answer to two decimal places.)

36.98 thousand dollars

(g) Find a 90% confidence interval for the annual salary of an individual with x = 7 job changes. (Round your answers to two decimal places.)

lower limit = 35.06 thousand dollars

upper limit = 38.89 thousand dollars

(h) Test the claim that the slope β of the population least-squares line is positive at the 5% level of significance. (Round your test statistic to three decimal places.)

t = 2.681

Find or estimate the P-value of the test statistic.

0.010 < P-value < 0.025

Conclusion Reject the null hypothesis. There is sufficient evidence that β > 0.

(i) Find a 90% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.) lower limit = 0.257

upper limit = 1.422

Interpretation

For each additional job change, the annual salary increases by an amount that falls within the confidence interval.