Question

A sample of scores for men and women from an examination in Statistics 201 were:

Men	78	69	45	81	72	82	84	46	58
Women	67	49	88	59	80	73	91	61	45

Given that the null hypothesis and the alternative hypothesis are:

  H₀: μ_m - μ_w ≤ 3
  H₁: μ_m - μ_w > 3

and using a 0.025 significance level conduct a t-test about a difference in population means:

a)

What is the correct decision rule?

	Reject H0 in favour of H1 if the computed value of the statistic is between -2.12 and 2.12.
	Reject H0 in favour of H1 if the computed value of the statistic is less than 2.12.
	Reject H0 in favour of H1 if the computed value of the statistic is less than -2.12 or greater than 2.12.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.12.
	None of the above.

b) Compute the pooled variance.
For full marks your answer should be accurate to at least four decimal places.

Pooled variance: 0

c) Compute the value of the test statistic.
For full marks your answer should be accurate to at least three decimal places.

Test statistic: 0

d)

What is your decision regarding H₀?

	There is sufficient evidence, at the given significance level, to reject H0, and accept H1 or at least there is not enough evidence to reject H1.
	There is insufficient evidence, at the given significance level, to reject H0.
	There is insufficient evidence to reject or not reject the null hypothesis.

Answer 1

a)

Reject H₀ in favour of H₁ if the computed value of the statistic is greater than 2.12.

b)

pooled variance =248.0556

c)

test statistic = -0.374

d)

There is insufficient evidence, at the given significance level, to reject H₀.