9. Cottonmouth Litter Size. Refer to Problem 8. Find a 98 % confidence interval for the difference between the mean litter sizes of cottonmouths in Florida and Virginia. Interpret your result.

The summary statistics on the data of the number of young per litter for 24 female cottonmouths in Florida and 44 female cottonmouths in Virginia is obtained as follows:

Here we assumed that the litter sizes of cottonmouths in both states are approximately normally distributed. Also the samples are independent and the population standard deviations are not known and are not assumed to be equal. Therefore we use nonpooled t-procedures in this illustration for comparing the differences of the population means.

Here we set up the null and alternative hypotheses as follows:

$H_0:{\mu }_1={\mu }_2$(There is no evidence to claim that, on average, the number of young per litter of cottonmouths in Florida is less than that in Virginia.)

Versus

$H_A:{\mu }_1<{\mu }_2$(There is no evidence to claim that, on average, the number of young per litter of cottonmouths in Florida is less than that in Virginia.)

This is a left-tailed test.

Also we set up $\alpha =0.01$level of significance.

Using MINITAB, we conduct the nonpooled t-test under the above stated null hypothesis as follows:

1 Choose Stat ? Basic Statistics ? 2-Sample t...

2 Select the Samples in different columnsoption button

3 Click in the First text box and specify Florida

4 Click in the Secondtext box and specify Virginia

5 Uncheck theAssume equal variances check box

6 Click the Options ... button

7 Click in the Confidence leveltext box and type 99

8 Click in theTest differencetext box and type 0

9 Click the arrow button at the right of theAlternative drop-down list box and select less than

10 ClickOK twice

The output for the above test is obtained as follows:

We observe that zero is not contained in the 98 % confidence interval of the difference between the two population means. Therefore we conclude that the two population means are different. Also we observe that the confidence interval is less than zero. Hence there is enough evidence to conclude that, on average, the number of young per litter of cottonmouths in Florida is less than that in Virginia.