Exam 11: Estimation: Describing a Single Population

The sample mean is an unbiased estimator of the population mean $\mu$ , and (when sampling from a normal population) the sample median is also an unbiased estimator of $\mu$ . However, the sample mean is relatively more efficient than the sample median.

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

A point estimate is defined as:

Which of the following statistical distributions is used when estimating the population mean when the population variance is known?

As a general rule, the normal distribution is used to approximate the sampling distribution of the sample proportion only if both n * $\hat { p }$ and n * $\hat { q }$ are at least five ( $\hat { q }$ = 1 - $\hat { p }$ ).

If the Student t distribution is incorrectly used instead of the Standard normal distribution when finding the confidence interval for the population mean, and the population variance was known, what will happen to the width of the confidence interval?

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 95% confidence interval estimate of the population mean, changing the sample size to 36.

The mean of the sampling distribution of the sample proportion $\hat { p }$ , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval $\mu$ :

Which of the following best describes an interval estimator? $\alpha$

The degrees of freedom used to find the t_/2 for a confidence interval for the population mean?

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 with a 99% confidence level?

How large a sample must be drawn to estimate a population proportion to within 0.03 with 95% confidence if we believe that the proportion lies somewhere between 25% and 45%?

Knowing that an estimator is unbiased only assures us that its expected value equals the parameter, but it does not tell us how close the estimator is to the parameter.

The upper limit of a confidence interval at the 99% level of confidence for the population proportion if a sample of size 100 had 40 successes is:

Which of the following is the width of the confidence interval for the population mean?

A random sample of size n has been selected from a normally distributed population whose standard deviation is s. In estimating an interval for the population mean, the t-distribution should be used instead of the z-test if:

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 95% confidence interval estimate of the population mean, changing the sample size to 300.

The percentage of the confidence interval relies on the significance level. $\alpha$

Which of the following statements is (are) true?