Question 3 This question is testing yourunderstanding of some important concepts about hypothesis testingand confidence intervals. For each part below, answer the question(1 mark) and then succinctly explain your reasoning (1 mark). (a)We are performing a one-sample t test at the 5% level ofsignificance where the hypotheses are 0 1 H VH :5 :5 µ µ = ? . Thenumber of observations is 15. State the critical value? (b) We areperforming a hypothesis test and we conclude that we reject H0 atthe 5% level of significance. Will we reject the same H0 (with thesame H1 ) at the 10% level of significance? (c) Suppose we areperforming a hypothesis test and we conclude that we cannot rejectH0 at the 5% level of significance. Can we reject the same H0 (withthe same H1 ) at the 10% level of significance? (d) Suppose we areperforming a two-sample proportion test at the 5% level ofsignificance where the hypotheses are 01 2 11 2 H p p VH p p : 0: 0?= ?? . The calculated p-value is 0.00268. Do we reject H0 ? (e)Based on the data, we obtain (1.85, 1.95) as the 95% confidenceinterval for the true mean. Can we reject 0 H : 0 µ = against 1 H :0 µ ? at the 5% level of significance?
