Question

In a sample of 58 business trips taken by employees in the HR department, a company finds that the average amount spent for the trips was $1,431 with a standard deviation of $459. In a sample of 83 trips taken by the employees in the sales department is $1,601 with a standard deviation of $580. When testing the hypothesis (at the 5% level of significance) that the variance of the amount spent on trips is significantly larger in one department than the other, what is the test statistic? (please round your answer to 2 decimal places)

Answer 1

Solution:

Since given sample sizes are large,we can assume sample standard deviations to be equal to population standard deviation .(Typically sample size is considered large when n 30 )

Test:   using two sample Z - test

Hypothesis test:

Sample 1	Sample 2
1431
= 459	= 580
= 58	= 83

Since Variances are known ,we use 2 sample Z-test

Standard Error:

  

Test Statistic = -1.939163