Solving By Hand Step 1 Set up hypotheses and determine level

Solving By Hand:

Step 1.            Set up hypotheses and determine level of significance

H₀: m₁=m₂ or H₀: m₁-m₂=0

H₁: m₁m₂

                  a=0.05

Step 2.             Select the appropriate test statistic.

Check s₁²/s₂² = 2.6²/2.9² = 0.80.

0.50<0.80<2 \\ assumption of equal variances is reasonable, and we can move forward with this method (we do not have to use exact methods).

                        .

Step 3.             Set up decision rule.

Reject H₀ if Z < -1.960 or if Z > 1.960.

Step 4.             Compute the test statistic.

= _____.

Now the test statistic,

      = ______.                                                                                 2.3

Step 5.             Conclusion.

Choose one of the alternatives below:

Do not reject H₀ because 4.13 > 1.960. We have statistically significant evidence at a=0.05 to show that the mean ages are not equal. The highest critical value we can reach without surpassing the Z-value of 4.13 is 3.819 (using the Two-Tailed Test a), the p-value is p<0.0001.

Reject H₀ because 4.13 > 1.960. We have statistically significant evidence at a=0.05 to show that the mean ages are not equal. The highest critical value we can reach without surpassing the Z-value of 4.13 is 3.819 (using the Two-Tailed Test a), the p-value is p<0.0001.

Solution

The correct answer is Reject H0 because 4.13 ( test statistic value) > 1.960 ( significant value)We have statistically significant evidence at a=0.05 to show that the mean ages are not equal. The highest critical value we can reach without surpassing the Z-value of 4.13 is 3.819 (using the Two-Tailed Test a), the p-value is p<0.0001.