E Question Help A politician daims that the mean salary for managers in his stat
ID: 3327011 • Letter: E
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E Question Help A politician daims that the mean salary for managers in his state is more than the national mean, $81.000. Assume the the population is normally distributed and the population standard deviation is $8700. The salaries (in dollars) for a random sample of 30 managers in the are listed. At -0.1, is there enough evidence to support the daim? Use technology 98,786- 71,645 79.588 87,378 98,894 78, 1 1 5 72,902 98.627 71,273 93,8 1 4 81.439 83,928 91,682 86,707 84.985 85,978 7 70,383 3 86.966 88 74300 8027 88,379 73.350 79.503 73,358 76,383 88.379 72,365 92,634 (a) Identify the null hypothesis and altermative hypothesis. OA. Ho: H81,000 Ha H$81.000 D. Ho -81,000 Ha : #81,000 O B. Ho: H281.000 Ha : 81,000 E. Ho'#81,000 Ha H-81,000 O C. Ho: A>81,000 Ha : $81,000 O F. Ho:u$81,000 Ha H81,000 (b) Identify the standardized test statistic (Round the final answer to two places as needed. Round all intermediate values to three places as needed) (c) Find the P-value. Use technology Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis O A. Reject H0 There is sufficient evidenoe to support the daimB. Fail to reed Ho. There is sufficient evidence to support the that managers mean salary is more than the national mean. claim that managers mean salary is more than the national mean. D. Fail to reject Ho. There is not suffi dent evidence to support the Rejed H0 There is not sufficient evidence to support the daim that managers mean salary is more than the national mean. O C. daim that managers mean salary is more than the national meanExplanation / Answer
(A) H0 : 81,000
Ha : > 81,000
Option F is correct here .
Population standard deviation = $ 8700
Standard error of sample mean se0 = /sqrt (n) = 8700/ sqrt(30) = $1588.40
(B) Here sample mean x = $ 82921.33
Test statsistic
Z = (82921.33 - 81000)/1588.40 = 1.2096
(C) p - value = Pr(Z > 1.2096) = 1 - Pr(Z < 1.2096) = 1- 0.8868 = 0.1132
so here a p - value is greater than significance level.
So we fail to reject H0 there is not sufficient evidence to support the caim that managers mean salary is more than the national mean.
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