Exam 11: Estimation: Describing a Single Population

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use?

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Determine the 90% confidence interval estimate of the population mean.

Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

The difference between the sample statistic and actual value of the population parameter is the percentage of the confidence interval.

Which of the following assumptions must be true in order to use the formula $\bar { x } \pm z _ { \mathfrak { w } / 2 } \sigma / \sqrt { n }$ to find a confidence interval estimate of the population mean?

A politician believes that the proportion of voters who will vote for a Coalition candidate in the 2004 general election is 0.65. A sample of 500 voters is selected at random. a. Assume that the politician is correct and p = 0.65. What is the sampling distribution of the sample proportion $\hat { p }$ ? Explain. b. Find the expected value and standard deviation of the sample proportion $\hat { p }$ . c. What is the probability that the number of voters in the sample who will vote for a Labor candidate in the 2004 general election will be between 340 and 350?

A 90% confidence interval estimate of the population mean $\mu$ can be interpreted to mean that:

Determine the minimum sample size required for estimating the population proportion of number of people who drive to work, to within 0.003, with 80% confidence.

The upper limit of the 90% confidence interval for $\mu$ , given that n = 64, $\bar { x }$ = 70 and $\sigma$ = 20, is 65.89.

A random sample of 10 waitresses in Darwin revealed the following hourly earnings (in dollars, including tips): 19 18 15 16 18 17 16 18 20 14 If the hourly earnings are normally distributed with a standard deviation of $4.5, estimate with 95% confidence the mean hourly earnings for all waitresses in Darwin.

We cannot interpret the confidence interval estimate of $\mu$ as a probability statement about $\mu$ , simply because the population mean is a fixed but unknown quantity.

Which of the following statistical distributions are used to find a confidence interval for the population proportion?

In developing an interval estimate for a population mean, the population standard deviation $\sigma$ was assumed to be 10. The interval estimate was 50.92 ± 2.14. Had $\sigma$ equaled 20, the interval estimate would have been:

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Interpret what the confidence interval estimate tells you.

When constructing a confidence interval estimate of $\mu$ , doubling the sample size n reduces the width %of the interval by half.

A robust estimator is one that:

A statistician wants to estimate the mean weekly family expenditure on clothes. He believes that the largest weekly expenditure is $650 and the lowest is $150. a. Estimate the standard deviation of the weekly expenditure. b. Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.

Which of the following statements is (are) correct?

The larger the level of confidence used in constructing a confidence interval, the wider the confidence interval.