A politician claims that the mean salary for managers in his state is more than the national
Question:
A politician claims that the mean salary for managers in his state is more than the national mean, $85,000. Assume the the population is normally distributed and the population standard deviation is $9000. The salaries (in dollars) for a random sample of 30 managers in the state are listed. At α=0.06, is there enough evidence to support the claim? Use technology.
83,588 | 98,467 | 87,600 | 81,090 | 84,281 | 72,665 | 83,032 | 82,046 | 95,101 | 82,544 | |
74,893 | 85,628 | 80,776 | 98,338 | 94,799 | 75,054 | 94,740 | 90,498 | 74,997 | 82,122 | |
70,621 | 90,122 | 95,565 | 79,472 | 73,946 | 98,535 | 85,361 | 98,813 | 96,342 | 96,506 |
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Part 1
(a) Identify the null hypothesis and alternative hypothesis.
A. H0:μ>85,000
Ha:μ≤85,000
B. H0: μ≤85,000
Ha: μ>85,000
C. H0: μ≥85,000
Ha: μ<85,000
D.
H0: μ=85,000
Ha: μ≠85,000
E. H0: μ≠85,000
Ha: μ=85,000
F. H0: μ>85,000
Ha: μ≤
Identify the standardized test statistic.
z=enter your response here (Round the final answer to two places as needed. Round all intermediate values to three places as needed.)
Part 3
(c) Find the P-value. Use technology. enter your response here (Round to three decimal places as needed.)
Part 4 (d) Decide whether to reject or fail to reject the null hypothesis.
A. Reject H0. There is sufficient evidence to support the claim that managers mean salary is more than the national mean.
B. Fail to reject H0. There is sufficient evidence to support the claim that managers mean salary is more than the national mean.
C. Reject H0.There is not sufficient evidence to support the claim that managers mean salary is more than the national mean.
D. Fail to reject H0. There is not sufficient evidence to support the claim that managers mean salary is more than the national mean.
Elementary Statistics Picturing The World
ISBN: 9780321911216
6th Edition
Authors: Ron Larson, Betsy Farber