Question

The null and alternate hypotheses are:

H₀ : μ₁ = μ₂
H₁ : μ₁ ≠ μ₂

A random sample of 12 observations from one population revealed a sample mean of 24 and a sample standard deviation of 3.8. A random sample of 8 observations from another population revealed a sample mean of 28 and a sample standard deviation of 3.7.

At the 0.01 significance level, is there a difference between the population means?

1. State the decision rule. (Negative values 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 value should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. State your decision about the null hypothesis.

• Do not reject H₀.

• Reject H₀.

5. The  p-value is

• between 0.05 and 0.02

• less than 0.001

• between 0.05 and 0.1

• between 0.001 and 0.01

• between 0.1 and 0.2

Answer 1

The statistical software output for this problem is:

Hence,

a) Decision rule:

Reject Ho if |t| > 2.878

Reject Ho if t < -2.878 or t > 2.878

b) Pooled estimate = 14.148

c) Test statistic = -2.330

d) Do not reject Ho

e) between 0.05 and 0.02

c) Test statistic = -2.330

d)