Question

A company’s auditor believes the per diem cost in Darwin rose significantly between 2005 and 2012. To test this belief, the auditor sampled 51 business trips from the company’s records for 2005; the sample average was $190 per day, with a population standard devi- ation of $18.50. The auditor selected a second random sample of 47 business trips from the company’s records for 2012; the sample average was $198 per day, with a population standard deviation of $15.60. If he uses a risk of committing a Type I error of 0.01, does the auditor find that the per diem average expense in Darwin has gone up significantly?

1. H_o: mu2005 - mu2012 (= ; <= ; >=)  0

H_a: mu2005 - mu2012 (< > ; > ; <) 0

2. Statistical test: (z / t)  test for 2 populations

3. Level of significance (be careful as to one-tailed or two-tailed)

4. Set up critical values (Write the value in the box, include "-" sign if negative, if two values, just write the positive one)

5. Gather sample data: xbar2005 =  ; n2005 = 51 ; sigma2005 = 18.5; xbar2012 = 198; n2012 = 47; sigma2012 =

6. Calculate test statistic (write your answer correct to 2 decimal places)

7. Make statistical conclusion: (Reject / Do not reject)  the null hypothesis. There is (sufficient/insufficient)   evidence that the per diem expense has rose significantly from 2002 to 2009 at 1% level of significance.

Answer 1

Let '1' represent 2005 and '2' represent 2012.

The claim is that the per diem expense rose up from 2005 to 2012. That means we are going to test whether the population mean 2012 is greater than mean 2005 or not. This is a one -tailed test since we are testing only on one side(greater than). Also we have been given the population SD so we can use z-test.

	2005 (1)	2012 (2)
n	51	47
	190	198
	18.50	15.60

Test

1.

  (The 2005 mean is less than 2012 mean)

  

  (The 2005 mean is greater than or equal to 2012 mean)

2. Statistical test: (z / t)  test for 2 populations

  z-test

This is because we have known population standard deviations

3. Level of significance (be careful as to one-tailed or two-tailed)

One -tailed

4. Set up critical values (Write the value in the box, include "-" sign if negative, if two values, just write the positive one)

Since it is one tail and we are using normal test we will look up for the critical value in normal probability table at p = 0.01

6. Calculate test statistic (write your answer correct to 2 decimal places)

Test statistic =

=

7. Make statistical conclusion: (Reject / Do not reject)  the null hypothesis. There is (sufficient/insufficient)   evidence that the per diem expense has rose significantly from 2002 to 2012 at 1% level of significance.

Since |Test Stat| < Critical value

Do not Reject the null hypothesis at 0.01 level of significance.\

There is insufficient evidence that the per diem expense has rose significantly from 2002 to 2012 at 1% level of significance.