A psychologist is testing whether two different therapies lead to different average stress reduction scores. In the first group, 99 patients have a mean reduction of 18.418.4 points (standard deviation 3.13.1). In the second group, 1111 patients have a mean reduction of 16.716.7 points (standard deviation 2.82.8). At the 0.050.05 significance level, what are the critical value(s) and the rejection region(s) for this test? Assume equal population variances.

Critical values: ±2.101\pm2.101Rejection regions: t−2.101t or 2.101"\u003et\u003e2.101t\u003e2.101

Critical values: ±2.086\pm2.086Rejection regions: t−2.086t or 2.086"\u003et\u003e2.086t\u003e2.086

Critical values: ±2.228\pm2.228Rejection regions: t−2.228t or 2.228"\u003et\u003e2.228t\u003e2.228

Critical values: ±2.064\pm2.064Rejection regions: t−2.064t or 2.064"\u003et\u003e2.064t\u003e2.064

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Problem 13Multiple Choice

A psychologist is testing whether two different therapies lead to different average stress reduction scores. In the first group, $9$ patients have a mean reduction of $18.4$ points (standard deviation $3.1$ ). In the second group, $11$ patients have a mean reduction of $16.7$ points (standard deviation $2.8$ ). At the $0.05$ significance level, what are the critical value(s) and the rejection region(s) for this test? Assume equal population variances.

Critical values: $\pm 2.086$

Rejection regions: $t is less than negative 2.086$ or $t is greater than 2.086$

Critical values: $\pm 2.101$

Rejection regions: $t is less than negative 2.101$ or $t is greater than 2.101$

Critical values: $\pm 2.228$

Rejection regions: $t is less than negative 2.228$ or $t is greater than 2.228$

Critical values: $\pm 2.064$

Rejection regions: $t is less than negative 2.064$ or $t is greater than 2.064$

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