"quantity"exercise:Sampling
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Questions 1:
Which of the following, holding all else constant, will most likely increase the width of the confidence interval for a parameter estimate?
A、 Reduction in the degree of confidence
B、 Increase in the sample size
C 、Use of the t-distribution rather than the normal distribution to establish the confidence interval
Questions 2:
An analyst collects the following set of 10 returns from the past:
The geometric mean return is closest to:
A 、10.89%.
B 、10.80%.
C、 9.62%.
C is correct. Reflecting the uncertainty of the unknown variance, confidence intervals based on the t-distribution will be larger than those using the normal distribution because t > z for any sample size, n, with the exception of n = ∞. Larger sample sizes and reduced confidence levels, holding all else constant, both reduce the width of a confidence interval. A is incorrect. A reduction in the degree of confidence will decrease the width of the confidence interval (because of a smaller reliability factor). B is incorrect. Increasing the sample size decreases the width of a confidence interval (because of a smaller standard error and, in the case of a t-distribution, of a smaller reliability factor).
B is correct. The geometric mean return is calculated as the Tth root of the product of T terms, where the terms are one plus the returns and T is the number of returns. After taking the Tth root, subtract one:
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