Question

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

boys	72	50	50	93	90	47	80	58
girls	74	98	45	70	67	56	64	91	72

Given that the null hypothesis and the alternative hypothesis are:

  H₀: μ_m - μ_w ≤ -1
  H₁: μ_m - μ_w > -1

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 less than -2.131 or greater 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 between -2.131 and 2.131.
	Reject H0 in favour of H1 if the computed value of the statistic is less than 2.131.
	None of the above.

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

Pooled variance: 0

c) Compute the value of the test statistic.
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

Given:

= 0.025

boys:

n1 = 8, = 67.50, S1 = 18.73

girls:

n2 = 9, = 70.78, S2 = 16.22

a)

Degrees of Freedom = n1+n2-2 = 8 + 9 -2 = 15

Critical value:

           ….....................…Using t table

ANSWER: B

B. Reject Ho in favour of H1 if the computed value of the statistic is greater than 2.131.

b)

Pooled Variance:

pooled Standard deviation = Sp =

C)

Test statistic:

d)

Conclusion:

Test statistic < Critical value, i.e. -0.505 < 2.131, That is Fail to reject Ho at 2.5% level of significance.

ANSWER: C

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