Question

12. As the number of degrees ot trdom ort d n s the the t distribution andd the standard nomal dist becomes larger b becomes smalter stays the same huctuates. d. 13. In interval esionation, thet distribution is applicatle ondy when a. the population has a mean of tess than 30 b. the sample standard deviation is used to estimate the population standard deviation the variance of the population is known d. the mean of the population is unknown. C. 14. From a population that is not normaly distributed and whose standard deviation is not known, a sample of 6 items is selected to develop an interval estimate for the mean of the population (4) The normal distribution can be used. The t distribution with 5 degrees of freedom must be used. The t distribution with 6 degrees of freedom must be used d. a. b. C. The sample size must be increased. 15. A 95% confidence interval for a population mean is determined to be 100 to 120. For the same data, if the confidence coefficient is reduced to .90, the confidence interval for u abecomes narrower. becomes wider. does not change. d. becomes 100.1 to 120.1. b. C. to .75. For the same data, if a is decreased, the confidence interval for the population proportion a. becomes narrower. b. becomes wider. uses a zero margin of error. remains the same. 16. Using an a = .04, a confidence interval for a population proportion is determined to be .65 C. d. 17. The ability of an interval estimate to contain the value of the population parameter described by the Laconfidence level. b. degrees of freedom. c. precise value of the population mean u. d. point estimate.

Answer 1

(12) (b) becomes smaller

> As degrees of freedom increase, the t-distribution converges to the standard normal distribution, hence the difference becomes smaller.

(13) (b) the sample standard deviation is used to estimate the population standard deviation.

> If population standard deviation is not known, we use t-distribution instead of z-distribution.

(14) (b) the t distribution with 5 degrees of freedom must be used.

> Sample size, n = 6. Hence, degrees of freedom = 6 - 1 = 5

(15) (a) becomes narrower.

> As the confidence level decreases, the corresponding z value decreases and thus we get a smaller margin of error or equivalently a narrow confidence interval.

(16) (b) becomes wider.

> As α decreases, the confidence level increases, and thus we get a wider confidence interval.

(17) (a) confidence interval.