Question

1. A sample of 25 seniors from a large metropolitan area school district had a mean Math SAT score of 450. Suppose we know that the standard deviation of the population of Math SAT scores for seniors in the district is 100. A 90% confidence interval for the population mean SAT score for the population of seniors is used. Which of the following would produce a confidence interval with a smaller margin of error?                                                                                                    (2)

1. Using a sample of 100 seniors
2. Using a confidence level of 95%
3. Using an alpha (α) of 0.01
4. Using a sample of only 10 seniors

2. In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are randomly selected for a market research campaign. What is the sampling distribution of their sample mean IQ? Must show work (explain) to justify choice.                                           (4)

1. exactly normal, mean 112, standard deviation 20
2. approximately normal, mean 112, standard deviation of 0.1
3. approximately normal, mean 112, standard deviation 1.414
4. approximately normal, mean 112, standard deviation 20

3. A final exam in Math 160 has a mean of 73 with a standard deviation of 7.8. If 34 students are randomly selected, find the probability that the mean of their test scores is more than 76.   (6)

4. Given that a piece of data is from a distribution with a mean of 0 and a standard deviation of 1, find the amount of area under the curve between z = – 1.83 and z = 0.                                 (3)

5. A study was conducted to estimate hospital costs for accident victims who wore seat belts. Twenty randomly selected cases to have a distribution that appears to be bell-shaped with a mean of $9004 and a standard deviation of $5629. Construct the 99% confidence interval for the mean of all such costs.                                                                                         

Answer 1