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%. | 
发表于 2009-6-6 18:44
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