Question

H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 10 observations from one population revealed a sample mean of 22 and a sample standard deviation of 3.7. A random sample of 7 observations from another population revealed a sample mean of 26 and a sample standard deviation of 5.0. The population standard deviations are unknown but assumed to be equal. At the 0.10 significance level, is there a difference between the population means? Required: a. State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.) b. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) c. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.) d. State your decision about the null hypothesis. multiple choice 1 Reject H0. Do not reject H0. e. The p-value is multiple choice 2 between 0.1 and 0.05. less than 0.001. between 0.02 and 0.05. between 0.001 and 0.01. between 0.1 and 0.2.

Answer 1

(a) Decision rule: reject null hypothesis if
`t < -1.753` or
`t > 1.753`, and fail to reject null hypothesis if
`-1.753\leq t\leq 1.753`

(b)
`s_(p)^(2)=18.214`

(c)
`t=-1.902`

(d) Reject
`H_(0)`

(e) The p-value is between 0.1 and 0.05

Explanation:

The explanation is attached below.