19. 31 and WA new type of speed trap camera is being evaluated to be und for detecting overspeeding vehicles. The current type of camera the of the has the probability of p-0.8 of a successful detection. From 4 successful. sample of 40 detections using the new cameras, 34 are found cains. on (a) Establish a 95% confidence interval for p. Find the (b) Can we conclude that the new type of camera is better? is brand buted How large a sample is needed in Question 12, if we wish to be 96% confident that our sample proportion will be within 0.02 of normal the true fraction of the voting population? 1 75 and 0 (taken 15 How large a sample is needed in Question 14, if we wish to be Landard 995 confident that our sample proportion will be within 0.05 of the true proportion of homes in the district that do not pay rent? ir final 16 A researcher is interested in a comparative study of stress among older executives and young executives. From a random sample or the of 500 older executives, 350 are suffering from stress; whereas of 4%. from a sample of 450 young executives, 300 are having stress s has a problems. Construct a 90% confidence interval for the difference normal between the proportion of older and young executives who are fidence suffering from stress. 17 Ten faculties of engineering at different universities were rchase surveyed. The sample contained 250 electrical engineering te the students, 80 being females and 175 civil engineering students, ducted 40 being females. Compute a 90% confidence interval for the veling difference between the proportions of female students in these The two fields of engineering. Is there a significant difference between the two proportions? 18 A car battery manufacturer claims that his batteries will last, on average, 3 years with a variance of 1 year. If 5 of these batteries dence have lifespans of 1.9, 2.4. 3.0, 3.5 and 4.2 years. construct a 95% confidence interval for o' and decide if the manufacturer's claim that o' = 1 is valid. Assume the population of the lifespans of the ound ulate batteries to be approximately normally distributed. ating 19 A random sample of 20 students obtained a mean of x = 68 and a variance of o' = 9 on a test in mathematics. Assuming the scores that are normally distributed, construct a 98% confidence interval for the 2 Construct a 90% confidence interval for of / o ; in Question 10.6 A random sample of 15 schoolchildren was taken and they (in kg) are 40, 35, 38, 41, 45. 44, 47. 50, 32, 33, 42, 46, 39, 31 48. Assuming the weights are approximately normal, estabien 95% confidence interval for the population mean weight of schoolchildren.6 A random sample of 15 schoolchildren was taken and the weights (in kg) are 40 35, 38, 4), 45, 44, 43, 50, 32, 33. $9, 31 and 48. Assuming the weights are approximately normal, establish a 95% confidence interval for the population mean weight of the schoolchildren. f 95 bottles of Vitamin C contains, on