Exam 11: Estimation: Describing a Single Population

A sample of size 300 is to be taken at random from an infinite population. Given that the population proportion is 0.70, the probability that the sample proportion will be smaller than 0.75 is: A. 0.9706. B. 0.4772. C. 0.4706. D. 0.9772.

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. What happens to the width of the confidence interval estimate when each of the following things happens? a. The confidence level increases. b. The confidence level decreases. c. The sample size increases. d. The sample size decreases. e. The value of the population standard deviation increases. f. The value of the population standard deviation decreases. g. The value of the sample mean increases. h. The value of the sample mean decreases.

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 99% confidence interval estimate of the population mean.

The sample size needed to estimate a population mean to within 2 units with a 95% confidence when the population standard deviation equals 8 is: A. 9. B. 61. C. 62. D. 8.

The width of the confidence interval estimate of the population mean $\mu$ is a function of only two quantities, the population standard deviation $\sigma$ and the sample size n.

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

A point estimate is defined as: A the average of the sample values. B the average of the population values. C a single value of an estimator. D an interval within which the population parameter is believed to lie.

The nighttime temperature readings for 20 winter days in Sydney are normally distributed with a mean of 5.5ºC and a population standard deviation of 1.5ºC. Determine the 90% confidence interval estimate for the mean winter nighttime temperature.

The z value for a 95% confidence interval estimate is: A. 2.12. B. 1.82. C. 2.00. D. 1.96.

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%?

The student t-distribution approaches the normal distribution as the: A number of degrees of freedom increases. B number of degrees of freedom decreases. C sample size decreases. D population size increases.

In an effort to identify the true proportion of first-year university students who are under 18 years of age, a random sample of 500 first-year students was taken. Only 50 of them were under the age of 18. The value 0.10 would be used as a point estimate to the true proportion of first-year students aged under 18.

The smaller the level of confidence used in constructing a confidence interval estimate of the population mean, the: A more likely that the confidence interval will contain the population mean. B wider the confidence interval. C narrower the confidence interval. D larger the sample required to estimate the popul ation mean to within a certain error bound.

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that: \begin{array}{|l|l|}\hline A&\text { n \hat{p} and \( n(1-\hat{p}) \) are both greater than 5 , where \( \hat{p} \) denotes the sample proportion. }\\\hline B&\text {\( n p \) and \( n(1-p) \) are both greater than 5 . }\\\hline C&\text {\( n \hat{p} \) and \( n(p+\hat{p}) \) are both greater than 5 . }\\\hline D&\text {the sample size is greater than 5 . }\\\hline \end{array}

Which of the following statements are correct? A If there are two unbiased estimators of a parameter, the one whose variance is larger is said to be relatively efficient. B If there are two unbiased estimators of a parameter, the one whose mean is larger is said to be relatively efficient. C If there are two unbiased estimators of a parameter, the one whose mean is smaller is said to be rel atively efficient. D If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

A marketing researcher wishes to determine the sample size needed to estimate the proportion of wine drinkers who prefer a certain brand of wine. How many wine drinkers should be surveyed if the researcher wants to be within 0.025 with 95% confidence?

In general, decreasing the confidence level ( $1 - \alpha$ ) will narrow the interval.

In the formula $\bar { x } \pm z _ { \alpha / 2 } \sigma / \sqrt { n }$ , the subscript $\alpha / 2$ refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

If the standard error of the sampling distribution of the sample proportion is 0.0229 for samples of size 400, then the population proportion must be either: A. 0.4 or 0.6. B. 0.5 or 0.5. C. 0.2 or 0.8. D. 0.3 or 0.7

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.