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2. A survey company is hired to estimate the proportion of county households that own three or more automobiles. They conducted their survey using a simple random sample of 250 randomly selected households and found that 23% of those households owned three or more automobiles. Answer the following questions, giving reasons for your answers. (24 pts) (a) Is the proportion, 23%. a parameter or a statistic? (b) If this survey company were to continually choose simple random samples of 100 randomly selected households. each time recording the proportion of household in the sample owning three or more automobiles, what would be the \"shape\" of the resulting distribution of all these sample proportions? (Before answering, check that up 2 10. n (I-p) 2 10) (c) [f we would like to construct a 95% confidence interval and would like the margin of error to be within 0.02, estimate the sample size n. (Use ,0 = 0.5) 3. State University requires an admission test of all its students. A simple random sample of 64 students from the University was selected to estimate the average test score of all University students. The average (mean) for the sample was found to be 3 =23.4 with a sample standard deviation of 3 =3.65. (20 pts) (a) Construct a 90% condence interval for the average (mean) test score of all University students. (Be specic about which formula you would use) (b) Interpret this condence interval in simple language. (c) Which of the following would result in a wider confidence interval for the average (mean) test score of all University students? (select all that apply) (i) Maintain the condence level at 95%. but increase the sample size. (ii) Maintain the condence level at 95%. but decrease the sample size. (iii) Keep the sample size at 64. but increase the confidence level to 99%. (iv) Keep the sample size at 64. but decrease the condence level to 90%