Question

This question concerns some concepts about hypothesis testing and confidence interval. For each part below, you must explain your answer. (a) Suppose we are doing a one-sample t test at the 5% level of significance where the hypotheses are H0 : ? = 0 vs H1 : ? > 0. The number of observations is 8. What is the critical value? [2 marks] (b) Suppose we are doing a hypothesis test and we can reject H0 at the 1% level of significance, can we reject the same H0 (with the same H1) at the 10% level of significance? [2 marks] (c) Suppose we are doing a hypothesis test and we cannot reject H0 at the 5% level of significance, can we reject the same H0 (with the same H1) at the 1% level of significance? [2 marks] (d) Suppose we are doing a two-sample proportion test at the 5% level of significance where the hypotheses are H0 : p1 - p2 = 0 vs H1 : p1 - p2 ? 0. The calculated test statistic is -1.21. Can we reject H0? [2 marks] (e) Based on the data, we obtain (0.53, 0.87) as the 95% confidence interval for the true mean. Can we reject H0 : ? = 0.5 against H1 : ? ? 0.5 at the 5% level of significance? [2 marks]

          This question concerns some concepts about hypothesis testing and confidence interval. For each part below, you must explain your answer.

(a) Suppose we are doing a one-sample t test at the 5% level of significance where the hypotheses are H0 : ? = 0 vs H1 : ? > 0. The number of observations is 8. What is the critical value? [2 marks]

(b) Suppose we are doing a hypothesis test and we can reject H0 at the 1% level of significance, can we reject the same H0 (with the same H1) at the 10% level of significance? [2 marks]

(c) Suppose we are doing a hypothesis test and we cannot reject H0 at the 5% level of significance, can we reject the same H0 (with the same H1) at the 1% level of significance? [2 marks]

(d) Suppose we are doing a two-sample proportion test at the 5% level of significance where the hypotheses are H0 : p1 - p2 = 0 vs H1 : p1 - p2 ? 0. The calculated test statistic is -1.21. Can we reject H0? [2 marks]

(e) Based on the data, we obtain (0.53, 0.87) as the 95% confidence interval for the true mean. Can we reject H0 : ? = 0.5 against H1 : ? ? 0.5 at the 5% level of significance? [2 marks]

This question concerns some concepts about hypothesis testing and confidence interval. For each part below, you must explain your answer.

(a) Suppose we are doing a one-sample t test at the 5% level of significance where the hypotheses are H0 : ? = 0 vs H1 : ? > 0. The number of observations is 8. What is the critical value? [2 marks]

(b) Suppose we are doing a hypothesis test and we can reject H0 at the 1% level of significance, can we reject the same H0 (with the same H1) at the 10% level of significance? [2 marks]

(c) Suppose we are doing a hypothesis test and we cannot reject H0 at the 5% level of significance, can we reject the same H0 (with the same H1) at the 1% level of significance? [2 marks]

(d) Suppose we are doing a two-sample proportion test at the 5% level of significance where the hypotheses are H0 : p1 - p2 = 0 vs H1 : p1 - p2 ? 0. The calculated test statistic is -1.21. Can we reject H0? [2 marks]

(e) Based on the data, we obtain (0.53, 0.87) as the 95% confidence interval for the true mean. Can we reject H0 : ? = 0.5 against H1 : ? ? 0.5 at the 5% level of significance? [2 marks]

Added by Christopher M.

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