TESTING
7.16 HYPOTHESIS 7-18 H0: = 31.5 ; H1: 31.5 n = 100 x = 29.8 s = 6.6; z = -2.575 . The p-value is approximately 0.01 Reject H0 at = 0.05 (and almost at = .01). H0: = 5 H1: 5 = .05 n = 120 x = 2.3 s = 1.5; z = -19.72 Reject H0 at = .05 and at smaller levels. Average miles traveled per day is probably smaller than 5. Changes in service may be necessary. = 4.3 H1: 4.3 H0: x = 3.8 s = 1.1 = .05; Reject H0 at any (p-value = 0.1454). n = 50 = 27 H0: H1: 27 n = 43 s = 4.954 x = 24.53 = .05; Critical value for right side: -1.96 z = -3.269. p-value = .0011. Reject H0, average staff age is under 27 years old. H0: = 0 H1: 0; n = 13 x = 3.1 s =1. t t = 11.177 The p-value is very small. Reject H0. Inclusion in the index likely increases average stock return (at least initially). = 2.5 H0: H1: 2.5 = 0.8 n = 20 x = 2.3 Use z because the population is normal and is known. z = -1.118 Do not reject H0 (p-value = 0.2636). H0: p = 0.42 H1: p 0.42 ^ x = 219 p = 219/550 = 0.39818use = .01; n = 550 .39818 - .42 z= = -1.037; Do not reject H0 (p-value = 0.2998). (.42)(.58) / 550 H0: u 7% H1: u < 7% n = 41 s = 2.9225 Reject H0, Americans do not save enough H0: p 0.17 n = 2,000 40 x = 2.405 = .01; z = -10.07
CHAPTER 7
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H1: p > 0.17 ^ x = 381 p = 381/2,000 = 0.1905 use = .01; z = 2.44 > 2.326
Reject H0 (p-value = .0073). The reported figure of 17% is probably not correct. ^ H0: p 0.11 H1: p < 0.11; n = 3,500 x = 421 p = 421/3,500 = 0.1203 ; z = +1.945 ^ Since p = .1203 > .11, we need not consider the test statistic value above. Do not reject H0 (p-value = 0.9741 > .05). There is no evidence that the unemployment rate has been reduced.
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x = 26.1 H0: = 25.2 H1: 25.2; n = 115 s = 3.2; z = 3.016 p-value 2(0.5 = - 0.4987) = 0.0026. Reject H0. The new model probably has a higher average electric output. (Template: Testing Difference in Means.xls, sheet: z-test from stats). Students don't need to submit this exercise. b) will result in an increase in the p-value. Statements a), b), c), and f) are all true; just different ways of saying the same thing. d) and e)
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are clearly false: for d) it is a Type I error that will be committed and for e) there is still the possibility of a Type I error being committed. ^ H0: p .30 H1: p > .30; N = 1,000 n = 166 x = 59 = .10; p = 59/166 = .3554 ^ p - p0 n/N = 166/1,000 = .166 > .05, z = p 0 q 0 N - n = 1.705 n N -1
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Reject H0 at = .05; p-value = .5 - .4559 = 0.0441. There is some evidence that over 30% of the Fortune top 1,000 use the multiple scenario approach. H0: = 125 H1: 125; n = 25 x = 151.96 s = 90.619; t = 1.4875 = .10. The critical points of t (24) are 1.711. There is no We cannot reject H0 even at evidence that the average price is different from $125 million. H0: p 0.20 H1: p < 0.20 ^ n = 5,000 x = 876 p = .1752; z = -4.38. The p-value is very small (p-value < .00003). Reject H0. There is strong evidence that the NSF study overestimated the proportion of foreign scientists employed by American laboratories. H0: =3 H1: 3 Reject H0 It takes longer than 3 seconds to print a page. p-value = 0.0030 H0: p 58% H1: p < 58%. Do not reject H0 at 0.05 level of significance (Using template: Testing Population Proportion.xls, sheet: Binomial). Reject H0 Ownership proportion is less than 50%. p-value = 0.000 H0: 40 H1: < 40. (Template: Testing Population Mean.xls, sheet: sample data) Do not reject H0 . H0: 4.2% H1: p < 4.2% Reject H0 at 0.01 level of significance
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