Exam 10: Introduction to Estimation

A sample of 49 measurements of tensile strength for roof hangers are calculated to have a mean of 2.45 and a standard deviation of 0.25. (Units are Newton's per square meter.) a.Determine the 95% confidence interval for mean tensile strength for all hangers. b.Interpret this confidence interval.

In developing an interval estimate for a population mean, a sample of 50 observations was used. The interval estimate was 19.76 $\pm$ 1.32. Had the sample size been 200 instead of 50, the interval estimate would have been:

Doubling the population standard deviation $\sigma$ has the effect of doubling the width of the confidence interval estimate of $\mu$ .

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 the standard deviation is changed to 50?

Define relative efficiency.

The difference between the sample statistic and actual value of the population parameter is the confidence level of the estimate.

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is

The sample variance (where you divide by n - 1) is an unbiased estimator of the population variance.

Suppose a sample size of 5 has mean 9.60. If the population variance is 5 and the population is normally distributed, the lower limit for a 92% confidence interval is 7.85.

An interval estimator estimates the value of an unknown ____________________.

A survey of 100 businesses revealed that the mean after-tax profit was $80,000. Assume the population standard deviation is $15,000: a.Determine the 95% confidence interval estimate of the mean after-tax profit for all businesses. b.Explain why you can use the confidence interval formula here, even though the population is not necessarily normal.

The sample variance is a point estimate of the population variance.

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 90% confidence interval estimate of the population mean.

If there are two unbiased estimators of a population parameter available, the one that has the smallest variance is said to be:

If you increase the confidence level, the confidence interval becomes ____________________.

The sample proportion $\tilde{ p }$ is a consistent estimator of the population proportion p because it is unbiased and the variance of $\tilde{ p }$ is p(1 - p) / n, which grows smaller as n grows larger.

The larger the confidence level, the:

Draw a sampling distribution of a biased estimator for $\mu$ .

An estimator is said to be consistent if:

NARRBEGIN: Conference Rooms Rented Conference Rooms Rented A hotel chain wants to estimate the average number of conference rooms rented daily in each month. The population of conference rooms rented daily is assumed to be normally distributed for each with a standard deviation of 24 rooms.NARREND -{Conference Rooms Rented Narrative} During February, a sample of 25 days has a sample mean of 37 rooms. Use this information to calculate a 92% confidence interval for the population mean.