Question

The average hourly paid for employees in food-service industries is currently $16.49. Suppose we take a sample of 45 employees to see if the average hourly paid differs from the claimed average of $16.49. The sample mean obtained is $17.91. Assume that the population standard deviation is $2.1 per hour. Conduct the hypothesis test at α=0.01 . State the hypotheses, test statistics, critical value, decision and conclusion. Round your numbers to 3 decimal places.

Answer 1

Solution:

Given

n= 45 sample size of employees.

. Population mean of hourly paid for employees in food service industry .

population standard deviations of hourly paid for employees in food service industry.

sample mean of hourly paid for employees in food service industry.

. Level of significance .

To test the hypothesis

. Vs.   

Test statistic

Z = 4.5360238

Test statistic Z = 4.536

The Z critical value at is

. From Z table

The Z critical value is 2.58

Decision : Z > Z critical value

4.536 > 2.58

Reject Ho .

Conclusion: Reject Ho , there is sufficient evidence to conclude that the average hourly paid differes from the $16.49 .