A state legislator wishes to survey residents of her district to see what proportion of the electorate is aware of her position on using state funds to pay for abortions. (Round your answers up to the nearest integer.) m USE SALT (a) What sample size is necessary if the 95% CI forp is to have a width of at most 0.14 irrespective of p? _x (b) If the legislator has strong reason to believe that at least % of the electorate know of her position, how large a sample size would you recommend to maintain a width of at most 0.14? -x On the basis of extensive tests, the yield point of a particular type of mild steel-reinforcing bar is known to be normally distributed with a = 100. The composition of the bar has been slightly modified, but the modification is not believed to have affected either the normality or the value of a. (a) Assuming this to be the case, if a sample of 16 modified bars resulted in a sample average yield point of 8449 lb, compute a 90% CI for the true average yield point of the modified bar. (Round your answers to one decimal place.) (:M:i)|b (b) How would you modify the interval in part (a) to obtain a confidence level of 96%? (Round your answer to two decimal places.) The value ofz v should be changed to |:]. A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specied conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design. (a) Define the parameter of interest. . a = true average braking distance for the new design 0 p1 = true average braking distance for the old design 0 f) = true proportion of cars whose braking distances did not reduce O 13 = true proportion of cars whose braking distances reduced V State the relevant hypotheses. O HO: y = 120 Ha: pi i 120 . H011\" = 120 Ha: pi 120 O Ho:f) = 120 Haj): 120 V (b) Suppose braking distance for the new system is normally distributed with o- = 11. Let )7 denote the sample average braking distance for a random sample of 36 observations. Which values of x are more contradictory to Ho than 117.2? O E 2 117.2 0 E s 117.2 'J What is the P-value in this case? (Round your answer to four decimal places.) :l What conclusion is appropriate if or = 0.10? I The new design does have a mean breaking distance less than 120 feet at 40 mph. O The new design does not have a mean breaking distance less than 120 feet at 40 mph. V (c) What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used? (Round your answer to four decimal places.) :l