## Answers

Lower bound = -2. 726

Upper bound = -0.163

Conclusion :

2nd option is correct.

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7.373 8.124 1.667 n 9 9 9 From the sample data, it is found that the corresponding sample means are: X1 = 58.889 X2 = 60.333 Also, the provided sample standard deviations are: 81 = 7.373 82 = 8.124 and the sample size is n = 9. For the score differences we have D = -1.444 SD = 1.667

(3) Test Statistics The t-statistic is computed as shown in the following formula: ta D sp/vn -1.444 1.667/9 -2.6 (4) Decision about the null hypothesis Since it is observed that t = 2.6 >te = 2.306, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p = 0.0316, and since p= 0.0316 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean mi is different than u2, at the 0.05 significance level. Confidence Interval The 95% confidence intervalis -2.726 < up < -0.163.