albeecho

Q1. Ryan McKeeler and Howard Hu, two junior statisticians, were discussing the relation between confidence intervals and hypothesis tests. During their discussion each of them made the following statement:

McKeeler: A confidence interval for a two-tailed hypothesis test is calculated as adding and subtracting the product of the standard error and the critical value from the sample statistic. For example, for a level of confidence of 68%, there is a 32% probability that the true population parameter is contained in the interval.

Hu: A 99% confidence interval uses a critical value associated with a given distribution at the 1% level of significance. A hypothesis test would compare a calculated test statistic to that critical value. As such, the confidence interval is the range for the test statistic within which a researcher would not reject the null hypothesis for a two-tailed hypothesis test about the value of the population mean of the random variable.

With respect to the statements made by McKeeler and Hu:

A)   both are correct.

B)   only one is correct.

C)   both are incorrect.

Correct answer is B)

McKeeler’s statement is incorrect. Specifically, for a level of confidence of say, 68%, there is a 68% probability that the true population parameter is contained in the interval. Therefore, there is a 32% probability that the true population parameter is not contained in the interval. Hu’s statement is correct.

Q2. Given a mean of 10% and a standard deviation of 14%, what is a 95% confidence interval for the return next year?

A)   -17.44% to 37.44%.

B)   -4.00% to 24.00%.

C)   -17.00% to 38.00%.

Correct answer is A)

10% +/- 14(1.96) = -17.44% to 37.44%.