Question

A random sample of 100 postal employees found that the average time these employees had worked for the postal service was x x = 7 years, with standard deviation s = 2 years. Assume the distribution of the time the population of employees has worked for the postal service is approximately normal, with mean μ μ . Are these data evidence that m has changed from the value of 7.5 years of 20 years ago? To determine this, we test the hypotheses H0: μ μ = 7.5, Ha: μ μ ≠ ≠ 7.5. What do you conclude regarding the value of the slope at the 1% significance level? Your answer should be either THE SLOPE IS ZERO or THE SLOPE IS NOT ZERO.

Answer 1

Solution :

= 7.5

= 7

s = 2

n = 100

This is the two tailed test .

The null and alternative hypothesis is

H0 :   = 7.5

Ha : 7.5

Test statistic = t

= ( - ) / s / n

= (7 -7.5) /2 / 100

= -2.5

P (t< -2.5 ) = 0.0141

P-value = 0.0141

= 0.01

0.0141 > 0.01

Do not reject the null hypothesis .

There is insufficient evidence to not conclude  regarding the value of the slope at the 1% significance level