The null and alternate hypotheses are: H0 : mu1 = mu2 H1 : mu1 not equal mu2 A random sample of 9 observations from one population revealed a sample mean of 22 and a sample deviation of 4.7. A random sample of 9 observations from another population revealed a sample mean of 26 and a sample standard deviation of 3.6. At the .10 significance level, is there a difference between the population means? (a) State the decision rule. (Negative values should be indicated by a minus sign. Round your answer to 3 decimal places.) The decision rule is to reject H0 if t < or t > (b) Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.) Pooled estimate of the population variance (c) Compute the test statistic.(Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.) Test statistic -2.027 (d) State your decision about the null hypothesis. Reject H0.

There is a difference between the population means at 0.10 significance level.

(a) The decision rule is to reject H0 if the test statistic (t) falls outside the region bounded by the critical values.

(b) Pooled estimate of the population variance is 17.525.

(c) Test statistic is -2.027

(d) Reject H0

Step-by-step explanation:

At 0.10 significance level, there is a difference between the population means because the null hypothesis is rejected.

(a) The decision rule is to reject H0 if the test statistic (t) falls outside the region bounded by the critical values.

(b) n1 = 9

s1 = 4.7

s1^2 = 4.7^2 = 22.09

n2 = 9

s2 = 3.6

s2^2 = 3.6^2 = 12.96

Pooled variance = [(n1-1)s1^2 + (n2-1)s2^2] ÷ (n1+n2-2) = [(9-1)22.09 + (9-1)12.96] ÷ (9+9-2) = 280.4 ÷ 16 = 17.525

(c) Test statistic (t) = (mean1 - mean2) ÷ sqrt[pooled variance (1/n1 + 1/n2)] = (22 - 26) ÷ sqrt[17.525(1/9 + 1/9)] = -4 ÷ 1.973 = -2.027

(d) degree of freedom = n1+n2-2 = 9+9-2 = 16

significance level = 0.10 = 10%

The test is a two-tailed test because the alternate hypothesis is expressed using not equal to.

critical values corresponding to 16 degrees of freedom and 10% significance level are -1.746 and 1.746

My decision rule:

Reject H0 because the test statistic -2.027 falls outside the region bounded by the critical values -1.746 and 1.746.

a - base

b - exponent

so,