A politician claims that the mean salary for managers in his state is more than the national mean, $82,000. Assume the population is normally distributed and the population standard deviation is $7600. The salaries (in dollars) for a random sample of 30 managers in the state are listed. At α = 0.07, is there enough evidence to support the claim? Use technology.
[91,290, 88,562, 72,096, 76,375, 82,569, 84,811, 91,290, 75,903, 79,729, 71,260], [79,850, 89,644, 99,708, 81,058, 92,850, 75,446, 74,968, 74,669, 87,482, 92,365], [83,477, 70,465, 86,220, 97,159, 77,672, 78,412, 83,441, 72,564, 85,735, 86,050]
(a) Identify the null hypothesis and alternative hypothesis.
A. H₀: μ > 82,000
Hₐ: μ ≤ 82,000
(b) Identify the standardized test statistic.
z =
A politician claims that the mean salary for managers in his state is more than the national mean, $82,000. Assume a random sample of 30 managers in the state are listed. At α = 0.07, is there enough evidence to support the claim? Use technology.
91,290 79,850 83,477
88,562 89,644 70,465
72,096 99,708 86,220
76,375 81,058 97,159
82,569 92,850 77,672
84,811 75,446 78,412
91,290 74,968 83,441
75,903 74,669 72,564
79,729 87,482 85,735
71,260 92,365 86,050
(a) Identify the null hypothesis and alternative hypothesis
A. H₀: 82,000 Hₐ: 82,000
B. H₊82,000 Hₐ=82,000
C. H₈2,000 Hₐ>82,000 F. H₌82,000 H₈2,000
D. H₉82,000 H₈2,000
E. H₈2,000 H<82,000
(b) Identify the standardized test statistic
(Round the final answer to two places as needed. Round all intermediate values to three places as needed.)