Conclusion of a Two-Sample T-Test

Question

The table provides summary statistics for a two-sample t-test comparing the means of Group X and Group Y. At a significance level of $$α = 0.05$$, what is the correct conclusion regarding the difference in means?

| Statistic                              | Group X | Group Y |
|----------------------------------------|---------|---------|
| Sample Size (n)                        | 30      | 30      |
| Sample Mean ($$\bar{x}$$)               | 100     | 105     |
| Sample Standard Deviation (s)          | 12      | 15      |
| Standard Error of Difference           | 4       |         |
| t-score                                | 1.25    |         |
| P-value                                | 0.215   |         |
| Significance Level                     | 0.05    |         |

Accepted Answer

Fail to reject $$H_0$$; no significant difference is detected.

Answer

Reject $$H_0$$; the difference is statistically significant.

Answer

Reject $$H_0$$; the t-score is significant.

Answer

Reject $$H_0$$; Group X has a significantly lower mean.

Answer

Reject $$H_0$$; Group Y has a significantly higher mean.

Statistic	Group X	Group Y
Sample Size (n)	30	30
Sample Mean ( $\bar{x}$ )	100	105
Sample Standard Deviation (s)	12	15
Standard Error of Difference	4
t-score	1.25
P-value	0.215
Significance Level	0.05

Conclusion of a Two-Sample T-Test

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