A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate? A) do not reject null (p .05) C) reject null (p

Question

A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?
A) do not reject null (p < .05)
B) do not reject null (p > .05)
C) reject null (p < .05)
D) accept null (p < .05)

Quizplus · Accepted Answer

In order to make a decision about whether to reject or fail to reject the null hypothesis, we need to compare the calculated value of the t-statistic to a critical value of t from a t-distribution table using the degrees of freedom (df) which is the sample size n minus 1 (df=28-1=27).

At α=.05 with two tails, the critical value for a t-distribution with 27 df is ±2.048. Since the calculated value of the t-statistic (2.13) is greater than the critical value of t (2.048), we reject the null hypothesis. This means that there is sufficient evidence to conclude that the population mean is not equal to the hypothesized value. Therefore, the most appropriate decision is to reject the null hypothesis, which is choice C.

A Researcher Tests the Mean of a Sample of 28