Question

A random sample of 1515 nursing students from Group 1 resulted in a mean score of 42.942.9 with a standard deviation of 2.82.8. A random sample of 1212 nursing students from Group 2 resulted in a mean score of 48.448.4 with a standard deviation of 5.15.1. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1μ1 represent the mean score for Group 1 and μ2μ2 represent the mean score for Group 2. Use a significance level of α=0.01α=0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 2 of 4 :  

Compute the value of the t test statistic. Round your answer to three decimal places.

Answer 1

H0: Null Hypothesis:

HA:Alternative Hypothesis:

Pooled Standard Deviation is given by:

The test Statistic is given by:

The test Statistic = - 3.569

=0.01

df = 15 + 12 - 2 = 25

From Table, critical value of t = - 2.485

Since calculated value of t = - 3.569 is less than critical value of t = - 2.485, the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that the mean score for Group 1 is significantly lower than the mean score for Group 2

Question asked:

Compute the value of the t test statistic. Round your answer to three decimal places.

The test Statistic = - 3.569