Question

A labor union claims that the mean income of its members is no more than $20,000 per year. The Employers' Association believes that this claim is too low and that the actual mean income is higher. A random sample of 64 union members yields a mean income of $20,278.50 with a standard deviation of $793.81. Calculate the standardized test statistic and find the P-value.

Answer 1

The null and alternative hypothesis is ,

The test is right tailed test.

Since , the population standard deviation is not known.

Therefore , use t-distribution.

Now , df=degrees of freedom=n-1=64-1=63

The p-value is ,

p-value= ; The excel function is , =TDIST(2.8067,63,1)

Decision : Here , p-value =0.0033<0.05 significance level.

Therefore , reject Ho.

Conclusion : There is not sufficient evidence to support the a  labor union claims that the mean income of its members is no more than $20,000 per year.