9.72 Business and Management The mean income per year of employees who produce i

Question

9.72 Business and Management The mean income per year of employees who produce internal and external newsletters and magazines for corporations was reported to be $51,500. These editors and designers work on corpora publications but not on marketing materials. As a result of poor economic conditions and oversupply, these corporate communications workers may be experiencing a decrease in salary. A random sample of 38 corporate communications workers revealed that x = 49,762. Conduct a hypothesis test to determine whether there is any evidence to suggest that the mean income per year of corporate communications workers has decreased. Assume 3750 and use = 0.01

Explanation / Answer

Here the reported mean income per year for employees H= $ 51,500

sample mean x = 49,762

sample size n = 38

Population standard deviation = 3,750

Hypothesizes are

Null Hypothesis : H0: There is no decrease in mean salary of employees. = $ 51500

Alternative Hypothesis : Ha : There is significant decrease in mean salary of employees . < $ 51500

The test is one tailed Z test.

Standard error of the sample mean se0= /sqrt(n) = 3750/ sqrt(38) = $ 608.33

Test statistic

Z = (x - H)/ se0 = (49762 - 51500)/ 608.33 = -2.857

p - value = Pr(Z < -2.857) = 0.0021 < 0.01

so p - value is less then the significance level alpha = 0.01 so we shall reject the null hypothesis and can conclude that there is significant decrease in employee's salary due to poor economic conditions and overupply.

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