In the past the average age of employees of a large corporation has been 40 year
ID: 3134739 • Letter: I
Question
In the past the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older indiviciduals. In order to determine whether there has been an increase in the average age of all the employees, a random sample of 25 employees was selected. The average age in the sample was 45 years with a standard deviation of 5 years. Assume the distribution of the population is normal. Let a = .05.
a. state the null and alternative null hypothesis
b. test to determine whether or not the mean age of all employees is significantly more than 40 years
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 40
Ha: u > 40 [ANSWER]
b)
As we can see, this is a right tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = + 1.644853627
Getting the test statistic, as
X = sample mean = 45
uo = hypothesized mean = 40
n = sample size = 25
s = standard deviation = 5
Thus, z = (X - uo) * sqrt(n) / s = 5
As z > 1.645, we REJECT THE NULL HYPOTHESIS.
Hence, the mean age of all employees is significantly more than 40 years at 0.05 level. [CONCLUSION]
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