A sample of 36 observations has a mean of 105 and a population standard deviation of 8. A second sample of 53 has a mean of 101 and a population standard deviation of 10. Conduct az-test about a difference in sample means using a 0.01 significance level and the following hypotheses:

H₀: ₁- ₂ 0

H₁: ₁- ₂> 0

a)What is the correct decision rule?

a. RejectH₀in favour ofH₁if the computed value of the statistic is between -2.33 and 2.33.

b. RejectH₀in favour ofH₁if the computed value of the statistic is less than 2.33.

c. RejectH₀in favour ofH₁if the computed value of the statistic is less than -2.33 or greater than 2.33.

d. RejectH₀in favour ofH₁if the computed value of the statistic is less than -2.58 or greater than 2.58.

e. RejectH₀in favour ofH₁if the computed value of the statistic is between -2.58 and 2.58.

f. RejectH₀in favour ofH₁if the computed value of the statistic is greater than 2.33.

g. 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:

c)What is your decision regardingH₀?

a. There is sufficient evidence, at the given significance level, to rejectH₀, and acceptH₁or at least there is not enough evidence to rejectH₁.

b. There is insufficient evidence, at the given significance level, to rejectH₀.

c. There is insufficient evidence to reject or not reject the null hypothesis.

d)Calculate thep-value.

For full marks your answer should be accurate to at least four decimal places.

P-value: