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 10 nursing students from Group 1 resulted in a mean score of 65.8 with a standard deviation of 5.1. A random sample of 16 nursing students from Group 2 resulted in a mean score of 70.4 with a standard deviation of 7.6. 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

here, i am doing 2 sample t test (assuming equal variance).

a).hypothesis:-

where, μ1 represent the mean score for Group 1 and μ2 represent the mean score for Group 2.

b).given data are:-

the pooled standard deviation be:-

  

the test statistic be:-

c).degrees of freedom :-

t critical value for df = 24, alpha= 0.05, left tailed test be:-

[ from t distribution table]

rejection rule:-

reject the null hypothesis if

decision:-

so, we fail to reject the null hypothesis.

d).conclusion:-

there is not sufficient evidence to conclude that the mean score for Group 1 is significantly lower than the mean score for Group 2 at 0.05 level of significance.

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