Exam 10: Introduction to Estimation

A random sample of 10 waiters in Weston, West Virginia, revealed the following hourly earnings, including tips: 19, 18, 15, 16, 18, 17, 16, 18, 20, and 14. (Units are dollars.) a.If the hourly earnings are normally distributed with a standard deviation of $4.50, estimate with 95% confidence the mean hourly earnings for all waitresses in Iowa City. b.Interpret your confidence interval.

Draw sampling distributions of a consistent estimator for $\mu$ where one sample mean is larger than the other.

NARRBEGIN: Time Spent Playing Comput Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.NARREND -{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 300.

The sample size needed to estimate a population mean to within 10 units was found to be 68. If the population standard deviation was 50, then the confidence level used was:

The sample size needed to estimate a population mean to within 50 units was found to be 97. If the population standard deviation was 250, then the confidence level used was

A random sample of 10 university students was surveyed to determine the amount of time spent weekly at the library. The times are: 13, 14, 5, 6, 8, 10, 7, 12, 15, and 3. If the times are normally distributed with a standard deviation of 5.2 hours, estimate with 90% confidence the mean weekly time at the library by all university students.

The sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 17.

Draw the sampling distribution of two unbiased estimators for $\mu$ , one of which is relatively efficient.

The version of the sample variance where you divide by ____________________ gives you an unbiased estimator of the population variance.

The confidence level that is considered to be the standard amongst statisticians is ____________________%.

Which of the following is not a characteristic for a good estimator?

If the population standard deviation is guesstimated, and it turned out to be larger than you assumed, then the sample size you calculated is ____________________ than it needs to be.

NARRBEGIN: Time Spent Playing Comput Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.NARREND -{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 36.

NARRBEGIN: Time Spent Playing Comput Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours.NARREND -{Time Spent Playing Computer Games Narrative} Determine and interpret the 99% confidence interval estimate of the population mean.

NARRBEGIN: College Dean College Dean A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200.NARREND -{College Dean Narrative} What sample size should be used if we wish to estimate the population mean to within 10 units?

Which of the following is an incorrect statement about a 90% confidence interval?

The sampling error for a confidence interval is also defined as the ____________________ of ____________________.

It is desired to estimate the average total compensation of CEOs in the publishing industry. Data were randomly collected from 18 CEOs and 95% confidence interval was calculated to be ($2,190,000, $4,720,000). Based on the interval above, do you believe the actual average total compensation of CEOs in the publishing industry could be $3,000,000?

____________________ estimators do not have the capacity to reflect the effects of larger sample sizes.

In determining the size n needed to estimate the population mean, n increases as the confidence level decreases.