Question

What conclusion can be drawn about these data given a t-value of 4.63 and a t(critical)-value of 1.782 at an a of 0.05?

1) The means are so different that a t-test is not needed to determine statistical significance.
2) The variances are significantly different because the t(critical)-value is smaller than the t-value.
3) The means are not significantly different because the t-value is larger than the t(critical)-value.
4) The means are significantly different because the t-value is larger than the t(critical)-value.

Answer 1

The correct conclusion is that the means are significantly different as the calculated t-value exceeds the critical t-value, leading to the rejection of the null hypothesis at the 0.05 significance level.

Step-by-step explanation:

The conclusion that can be drawn about the data given a t-value of 4.63 and a t(critical)-value of 1.782 at an α of 0.05 is that the means are significantly different because the t-value is larger than the t(critical)-value. In hypothesis testing, when the absolute value of the t-value is greater than the t(critical)-value at a given significance level (α), we reject the null hypothesis. Here, since 4.63 > 1.782, we have enough evidence to conclude that there is a statistically significant difference between the means being tested.