Question

The manager of Tile Central believes that the Virginia store is more profitable, in terms of weekly profit per full-time employee, than the Clayfield store. Random samples of size 17 and 16 accounting records for Clayfield and Virginia, respectively, were taken. These yielded average weekly profit per full-time employee for Clayfield and Virginia of $278.80 and $304.68, respectively, and variances of 881.32 and 993.45 dollars squared.

It is assumed that the population variances are equal and the distribution of weekly profit per full time employee for both stores approximates a normal distribution. Use alpha = 0.01.

1. If the hypotheses are to be written as Clayfield minus Virginia, what is the direction of the alternative hypothesis? Type the letters gt (greater than), ge (greater than or equal to), lt (less than), le (less than or equal to) or ne (not equal to) as appropriate in the box.

2. Determine the standard error for the difference between means, reporting your answer to three decimal places.

3. Calculate the test statistic, reporting your answer to two decimal places.

4. Is the null hypothesis rejected for this test? Type yes or no.

5. Regardless of your answer for 4, if the null hypothesis was rejected, can we conclude that the manager's claim is valid at the 1% level of significance? Type yes or no.

Answer 1

Let population 1 is weekly profit per full-time employee for Clayfield and population 2 is weekly profit per full-time employee for Virginia.

The sample standard deviations are:

1:

Here hypothesis test is left tailed. The alternative hypothesis is

That is Ha: mu1 - mu2 lt 0

2:

The standard error is

3:

4:

Yes the null hypothesis is rejected.

5:

There is evidence to support the manager's claim at 1% level of significance.

Answer: yes