Question

A group of 16 students in the teacher credentialing program calculated their mean test score to be 91%. The entire class mean was 88%, with a standard deviation of 4.43. Assuming a significance level of 0.05, what should you conclude?

A) Fail to reject the null hypothesis
B) Reject the null hypothesis
C) Insufficient information
D) The test is inconclusive

Answer 1

To determine whether to reject or fail to reject the null hypothesis, perform a hypothesis test.

Step-by-step explanation:

To determine whether to reject or fail to reject the null hypothesis, we need to perform a hypothesis test.

Null Hypothesis (H0): The mean test score for the group of 16 students is equal to the entire class mean of 88%.

Alternative Hypothesis (H1): The mean test score for the group of 16 students is not equal to the entire class mean of 88%.

Next, we calculate the test statistic:

Z = (sample mean - population mean) / (population standard deviation / sqrt(n))

Z = (91 - 88) / (4.43 / sqrt(16))

Z = 1.35

Looking up the critical value for a significance level of 0.05 in the Z-table, we find that the critical value is approximately 1.96.

Since the test statistic (1.35) is less than the critical value (1.96), we fail to reject the null hypothesis. This means that there is insufficient evidence to conclude that the mean test score for the group of 16 students is different from the entire class mean.

Therefore, the answer is A) Fail to reject the null hypothesis.