A Psychologist Has Established What She Calls Her Generalized Anxiety Ga Scale The Ga Scale Which Is A Scale From 0 1 (262.69 KiB) Viewed 102 times
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 11 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=8.50-0.21x (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 0.07. Is there a significant linear relationship between the two measures? Do a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 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 H₁₂. Ho 0 : H₁ :0 1 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) (e) Based on our data, can we conclude (using the 0.05 level) that there is a significant linear relationship between mean sleep time over the past seven nights and GA score? Yes No В Р μ X ロミロ O>O X ロ=ロ ☐#0 OSO O<O ?
A health policy economist interested in investigating the relationship between the cost of prescription drugs in Canada and the cost of prescription drugs in the United States has information from a random sample of 55 prescription drugs sold in both countries. For each of these drugs, the economist is examining two pieces of information: the average cost x (in Canadian dollars) of a one-month supply of the drug in Canada, and the average cost y (in U.S. dollars) of a one-month supply of the drug in the United States. The economist finds that for the sample of drugs examined, the least-squares regression equation relating x and y is y=-0.59+0.81x. The economist also finds that the standard error of the slope of the least-squares regression line is approximately 0.31. Test for a significant linear relationship between x and y by doing a hypothesis test regarding the population slope B₁. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.05 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 H₁. HO H₁:0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) 0 (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Based on the data, can the economist conclude (using the 0.05 level) that there is a significant linear relationship between the average prescription drug cost in Canada and the average prescription drug cost in the United States? Yes No В P |x Olo ロマロ O<O X ロ=ロ 0#0 G μ 00 OSO O>O ?
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