1-7 fill in the blanks

1. As the sample size increases, the standard error of the mean----------------------------

2. The probability distribution of ALL POSSIBLE values of the sample proportion is called the:-------------------------------------------------

3. For a Normal probability distribution, a negative value of Z indicates that the Z value is to the ----------- of the mean.

4. A standard normal probability distribution is a normal distribution with a mean of ---------------, and a standard deviation of -------------.

5. The standard error is the difference between the value of the -------------mean, and the value of the --------------mean.

6. As the number of degrees of freedom for a t distribution decreases, the difference between the t distribution and the standard normal distribution ------------------------.

7. If we change a 99% confidence interval estimate to a 95% confidence interval estimate, we can expect the size of the confidence interval to -----------------.

8-12 Show All Work

8. The U.S. Department of Transportation reported the results of a survey of driving safety. In a random sample of 1000 drivers, 275 were using their cell phone. Compute and explain a 99% confidence interval estimate of the population proportion of drivers who use their cell phone while driving.

9. According to an IRS study, it takes a mean time of 330 minutes for taxpayers to prepare, copy and electronically transfer a 1040 tax form. The population standard deviation of this distribution is 75 minutes. A consumer watchdog agency selects a random sample of 65 taxpayers for further study.

A. What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample mean for samples of size 65?

B. What is the probability that the sample mean is greater than 320 minutes?

10. Grades on a final exam in Economics are normally distributed with a mean of 71 and a standard deviation of 11.

A. What is the probability that a randomly selected student will receive a score greater than 80?

B. What is the probability that a randomly selected student will score less than 60 and fail the exam?

C. If the top 10% of scores receive a grade of "A", what is the minimum score needed to get an "A"?

11. Assume that the population proportion of all business professionals who select an airline based on price is 0.30. A random sample of 215 business professionals is to be used for further study.

A. What is the shape, mean(expected value), and standard deviation of the sampling distribution of the sample proportion for samples of size 215?

B. What is the probability that our sample of 215 results in a sample proportion that falls within 4 percent (+/- 0.03) of the population value?

12. Health insurers are putting pressure on hospitals to reduce the average "length of stay" of their patients. A random sample of 27 hospitals in one state had a sample mean "length of stay" for men of 4.1 days and a sample standard deviation of 1.85 days. Compute and explain a 99% confidence interval estimate of the population mean "length of stay" for men in that state.