Question

The researcher conducted a hypothesis test and found the 95% confidence interval to examine whether there is a difference in high school students completion rate in percent with respect to the size of the teachers' salary (low or medium). The hypothesis test result showed p-value of 0.59 and the CI was [-2.45, 4.45].

In the space provided below,

a) Explain whether the hypothesis test result and the confidence interval are in agreement.

b) Explain whether and why Type 1 error or Type 2 error could occur in this study.

Answer 1

The researcher conducted a hypothesis test and found the 95% confidence interval to examine whether there is a difference in high school students completion rate in percent with respect to the size of the teachers' salary (low or medium). The hypothesis test result showed p-value of 0.59 and the CI was [-2.45, 4.45].

Here we want to test for difference between high school students completion rate in percent with respect to the size of the teachers' salary (low or medium.So the hypothesis are as follows

Null: There is no difference between high school students completion rate in percent with respect to the size of the teachers' salary (low or medium). That is the difference = 0.

Alternative: There is a difference between high school students completion rate in percent with respect to the size of the teachers' salary (low or medium).That is the difference does not equal 0.

The level of significance = 1 -0.95 = 0.05

In the space provided below,

a) Explain whether the hypothesis test result and the confidence interval are in agreement.

If testing with confidence interval, we check if the null value lies in the interval. If yes then we do not reject the null hypothesis.

Here the interval [-2.45, 4.45] contains '0' so the null difference is there. So we do not reject the null hypothesis and conclude that there is no difference with 95% confidence.

In terms of p-value, we reject the null hypothesis if p-value < level of significance.

p-value = 0.59 > 0.05

So we do not reject the null hypothesis.

With both approaches we are not reject the null hypothesis at same significance level (0.05).

b) Explain whether and why Type 1 error or Type 2 error could occur in this study.

Error depends on the conclusion whether reject or fail to reject the null hypothesis.

Type 1 : Reject true null hypothesis

Type 2: Accept false null hypothesis.

Conclusion: Do not reject null hypothesis.

Here the conclusion suggests that there is a possibility of accepting a false null hypothesis.

Therefore there is a possibility of making type 2 error.

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