Question

A sample of 42 observations has a mean of 103 and a population standard deviation of 7. A second sample of 61 has a mean of 100 and a population standard deviation of 9. Conduct a z-test about a difference in sample means using a 0.04 significance level and the following hypotheses:

  H₀: μ₁ - μ₂ = 0
  H₁: μ₁ - μ₂ ≠ 0

a)

What is the correct decision rule?

	Reject H0 in favour of H1 if the computed value of the statistic is between -1.75 and 1.75.
	Reject H0 in favour of H1 if the computed value of the statistic is less than -2.05 or greater than 2.05.
	Reject H0 in favour of H1 if the computed value of the statistic is between -2.05 and 2.05.
	Reject H0 in favour of H1 if the computed value of the statistic is less than 2.05.
	Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.05.
	Reject H0 in favour of H1 if the computed value of the statistic is less than -1.75 or greater than 1.75.
	None of the above.

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

Test statistic: 0

c)

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.

d) Calculate the p-value.
For full marks your answer should be accurate to at least four decimal places.

P-value: 0

Answer 1