Question

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

Men	62	91	92	77	69	86	64	60	94
Women	51	79	62	88	80	50	87	65

Given that the null hypothesis and the alternative hypothesis are:

  H₀: μ_m - μ_w = -5
  H₁: μ_m - μ_w ≠ -5

and using a 0.05 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 -2.131 and 2.131.
	Reject H0 in favour of H1 if the computed value of the statistic is less than 2.131.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.131.
	Reject H0 in favour of H1 if the computed value of the statistic is less than -2.131 or greater than 2.131.
	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 less than -2.131 or greater than 2.131.

b)

pooled variance =212.0704

c)

test statistic =1.692

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