Help to explain how to get to the answer and the steps involved.

6.12 Is college worth it? Part I. H0: p = 0.50 HA: p < 0.50 n=331 SE = √0.50(1 -0.50)/331 = 0.027 39 Z = (.48 -.50)/0.027 39 = -.7302 α = 0.05 p-value:(Z < -0.73)= 0.2327 Since p ≥ α (0.2327 ≥ 0.05), we do not have enough evidence to reject the null hypothesis . There is not enough evidence to suggest that a minority of Americans who decide no t to attend college do so because they c an ’t afford it. (b) Would you expect a confidence interval for the proportion of American adults who decide not to go to college because they cannot a fford it to include 0.5? Explain. Yes, because the confidence interval and the hypothesis test usually get to the same conclusion. In this case assuming the alpha level = 0.05 and the confidence interval is 95%: .48±1.96*0.2739 (0.4263156, 0.5336844) 0.50 is included in this interval. 6.22 Sleep deprivation, CA vs. OR, Part I. Calculate a 95% confidence interval for the difference between the proportions of Californians and Oregonians who are sleep deprived and interpret it in context of the data. nCA =11,545 nOR =4691 p^ CA =.08 p^ OR =0.088 p^ OR - p^ CA = 0.088 – 0.08 = 0.008 p^ difference = 0.008 SE = √0.08(1 -0.08)/ 11,545 + 0.088(1 -0.088)/4691 sqrt( (0.08*.92/11545)+(0.088*.912)/4691) = 0.004845984 0.008±1.96*0.0048 (-0.017408 , 0.001408 ) We 95% confident that the difference between the proportion of residents in Oregon and California that report insufficient sleep is between -0.017408 and 0.001408 . 6.24 Sleep deprivation, CA vs. OR, Part II. (a) Conduct a hypothesis test to determine if these data provide strong evidence the rate of sleep deprivation is different for the two states. (Reminder: Check conditions) Conditions: Sample populations can be assumed to be independent p^ pool =0.0823 and (1 -0.0823) multiplied by each n yields a number > 10 We can use a pooled proportion because the null hypothesis assumes pOR = pCA (or 0 difference) H0: pOR - pCA = 0 HA: pOR - pCA ≠ 0 p^ OR - p^ CA = 0.088 – 0.08 p^ difference = 0.008 p^ pool =0. 0823 SE = sqrt((0.0823*.9177/11545)+(.0823*.9177/4691)) = 0.004758391 Z= p^ difference - p0 /SE =(0.008 -0)/0.0047 6 =1.68 α = 0.05 2*pnorm(1.68,lower.tail = FALSE) p-value = 0.09 Fail to reject the null hypothesis. The data do not provide strong evidence the rate of sleep deprivation is different for the two states . (b) It is possible the conclusion of the test in part (a) is incorrect. If this is the case, what type of error was made? Yes, it is possible. This would be a Type II error.