A psychologist has established what she calls her Generalized Anxiety (GA) scale. The GA scale, which is a scale from 0 to 10, measures the "general anxiety" of an individual, with higher GA scores corresponding to more anxiety. Suppose that, as sleep researchers, we're interested in finding out if there is a significant relationship between individuals' sleep behavior and their GA scores. We randomly sample o adults, recording the mean number of hours of sleep for each over the previous seven nights. We also measure the GA score for each adult. Suppose that the least-squares regression equation relating the two measures is y - 7.98-0.28x (with x denoting mean sleep time and y denoting GA score). Suppose also that the standard error of the slope of this least-squares regression line is approximately 0.17. Is there a significant linear relationship between the two measures? Do a hypothesis test regarding the population slope . (Assume that the variable y follows a normal distribution for each value of X and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H . P H :0 (b) Determine the type of test statistic to use. Degrees of freedom: 020 0=0 030 (c)/ Find the value of the test statistic. ( Round to three or more decimal places.) (d) Find the two critical values at the 0.10 level of significance. (Round to three or more decimal places.) X 5 and (e) Based on our data, can we conclude (using the 0.10 level) that there is a significant linear relationship between mean sleep time over the past seven nights and GA score? Yes No

Answer rating: 100% (QA)

The Answer is in the image, click to view ... View the full answer