Question

A study was designed to compare the attitudes of two groups of nursing students towards computers. Group 1 had previously taken a statistical methods course that involved significant computer interaction. Group 2 had taken a statistic methods course that did not use computers. The students' attitudes were measured by administering the Computer Anxiety Rating Scale (CARS). A random sample of 16 nursing students from Group 1 resulted in a mean score of 41.4 with a standard deviation of 6.5. A random sample of 12 nursing students from Group 2 resulted in a mean score of 52.6 with a standard deviation of 5.8. Can you conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2? Let μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.

Step 4 of 4: State the test's conclusion.

Answer 1

Step 1 of 4:

H0: Null Hypothesis: ( Mean score for Group 1 is not significantly lower than the mean score for Group 2)

HA:Alternative Hypothesis: ( Mean score for Group 1 is significantly lower than mean score for Group 2) (Claim)

Step 2 of 4:

n1 = 16

1 = 41.4

s1 = 6.5

n2 = 12

2 = 52.6

s2 = 5.8

Pooled Standard Deviation is given by:

Test Statistic is given by:

Step 3 of 4:

= 0.05

df = 16 +12 - 2 = 26

From Table, critical value of t = - 1.706

Decision Rule:
Rejct H0 if t < - 1.706

Step 4 of 4:
Since calculated value of t = - 4.420 is less than critical value of t = - 1.706, the difference is significant. Reject null Hypothesis.

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