Question

The null and alternate hypotheses are: H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 11 observations from one population revealed a sample mean of 25 and a sample standard deviation of 3.5. A random sample of 4 observations from another population revealed a sample mean of 29 and a sample standard deviation of 4.5. At the 0.01 significance level, is there a difference between the population means?

State the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

2. Compute the pooled estimate of the population variance. (Round your answer to 3 decimal places.)

3. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

Answer 1

Given that

sample size n1 = 11

sample mean xbar_1 = 25

sample standard deviation s_1 = 3.5

sample size n2 = 4

sample mean xbar_2 = 29

sample standard deviation s_2 = 4.5

(A) degree of freedom = n1+n2 -2

= 11+4-2

= 13

significance level = 0.01

t critical = T.INV.2T(alpha,df) = T.INV.2T(0.01,13) = 3.012

Decision rule: Reject null hypothesis test statistic t < -3.012 or t > 3.012

(B) Pooled variance

(C) test statistic t is given as