b Equal-variances estimator = (524 – 469) 2.009 = 55 146.33 c The interval widens. d Equal-variances estimator = (524 – 469) 1.972 = 55 36.26 e The interval narrows.
13.6 = 0 0 a Equal-variances test statistic
Rejection region: –2.074 or 2.074 = = .43, p-value = .6703. There is not enough evidence to infer that the population means differ.
b Equal-variances test statistic
Rejection region: –2.074 or 2.074 = = .04, p-value = .9716. There is not enough evidence to infer that the population means differ. c The value of the test statistic decreases and the p-value increases. d Equal-variances test statistic
Rejection region: –1.960 or 1.960 = = 1.53, p-value = .1282. There is not enough evidence to infer that the population means differ. e The value of the test statistic increases and the p-value decreases. f Rejection region: –2.074 or 2.074 = = .72, p-value = .4796. There is not enough evidence to infer that the population means differ. g The value of the test statistic increases and the p-value decreases.
13.7 a Unequal-variances estimator = 64.8 (rounded to 65, approximated by ) = (63 – 60) 1.667 = 3 4.59
b Unequal-variances estimator = 63.1 (rounded to 63, approximated by ) = (63 – 60) 1.671 = 3 10.38 c The interval widens. d Unequal-variances estimator = 131 (approximated by ) = (63 – 60) 1.656 = 3 3.22 e The interval narrows.
13.8 = 0 0 a Unequal-variances test statistic = 200.4 (rounded to 200)
Rejection region: = = .62, p-value = .2689. There is not enough evidence to infer that is greater than . b Unequal-variances test statistic = 223.1 (rounded to 223)
Rejection region: = = 2.46, p-value = .0074. There is enough evidence to infer that is greater
