12. Based on the performance of all individuals who tested between July 1, 2012 and June 30, 2015, the GRE Verbal Reasoning scores are normally distributed with a mean of 150 and a standard deviation of 8.45.( https:// www. ets. org / s / gre / pdf / gre _ guide _ table1a. pdf). Show all work. Just the answer, without supporting work, will receive no credit.
( a) Consider all random samples of 36 test scores. What is the standard deviation of the sample means?
( b) What is the probability that 36 randomly selected test scores will have a mean test score that is between 148 and 152?
13. An insurance company checks police records on 500 randomly selected auto accidents and notes that teenagers were at the wheel in 80 of them. Construct a 95 % confidence interval estimate of the proportion of auto accidents that involve teenage drivers. Show all work. Just the answer, without supporting work, will receive no credit.
14. A city built a new parking garage in a business district. For a random sample of 60 days, daily fees collected averaged $ 2,000, with a standard deviation of $ 400. Construct a 95 % confidence interval estimate of the mean daily income this parking garage generates. Show all work. Just the answer, without supporting work, will receive no credit.
15. ABC Company claims that the proportion of its employees investing in individual investment accounts is higher than national proportion of 45 %. A survey of 200 employees in ABC Company indicated that 100 of them have invested in an individual investment account.
Assume we want to use a 0.10 significance level to test the claim.
( a) Identify the null hypothesis and the alternative hypothesis.
( b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.