Question

True/False. a. _______ If the alternative (research) hypothesis Ha is accepted at the .05 level of significance, then it would also be accepted at the .10 level of significance. b. _______ If the null hypothesis Ho is not rejected, one can conclude that Ho is true. c. _______ When the power of a hypothesis test decreases, the probability of making a Type II error increases. d. _______ If the null hypothesis Ho is rejected, then the results are considered statistically significant. e. _______ Increasing sample sizes tends to decrease the widths of confidence intervals. f. ________ Decreasing the level of confidence tends to decrease the widths of confidence intervals.

Answer 1

a) If the alternative (research) hypothesis Ha is accepted at the .05 level of significance, then it would also be accepted at the .10 level of significance. - TRUE

Reason: If the p-value is lower than the significance level we chose, then we reject the null hypotheses Ho, in favour of the alternative hypothesis Ha . As we accepted the alternative hypothesis in this context, implies p-value < 0.05, of course p-value < 0.10. Hence Ha will also be accepted at the .10 level of significance.

b) If the null hypothesis Ho is not rejected, one can conclude that Ho is true. - TRUE

Reason: If there is not enough evidence, we do not reject the null hypothesis, it implies the null hypothesis Ho is true.

c) When the power of a hypothesis test decreases, the probability of making a Type II error increases. - TRUE

Reason: The power of a hypothesis test is nothing more than 1 minus the probability of a Type II error. Hence if power decreases the Type II error increases.

d) If the null hypothesis Ho is rejected, then the results are considered statistically significant. -TRUE

Reason: If there is sufficient evidence (“beyond a reasonable doubt”), we reject the null hypothesis implies the results are statistically significant (i.e., not likely to happen by chance).

e) Increasing sample sizes tends to decrease the widths of confidence intervals. - TRUE

Reason: The confidence interval is given by- Point estimate Margin of error  

And margin of error is inversely proportional to sample size(as standard error is inversely proportional to sample size). Hence the width of confidence interval decreases as sample size increases.

f) Decreasing the level of confidence tends to decrease the widths of confidence intervals. - TRUE

Reason: As we decrease the confidence level, the z- multiplier decresese (t-multiplier decreases), and hence the width of the interval decreases.