Which of the following is/are true about the Central Limit Theorem?
Answer(s): D
The Central Limit Theorem states that for a population with mean M and variance S, a sample of large size n has a sampling distribution of mean which is approximately normal with mean M and variance S/n.
Which of the following is the formula for the covariance between X and Y?
Answer(s): B
E[(X - E(X))*(Y - E(Y))] is the covariance between X and Y.
A sample of the amounts spent to heat all-electric homes of similar sizes in March revealed these amounts (to the nearest dollar): $212, $191, $176, $129, $106, $92, $108, $109, $103, $121, $175 and $194. What is the range?
Answer(s): C
Range = 212 - 92 = 120
A dataset of 105 observations is organized in a relative frequency distribution into 9 classes. The sum of the relative frequencies across all the classes equals ________.
Relative class frequencies are percentages and across all classes, they must sum up to 100%, which is the same as summing up to 1.00.
A portfolio manager has estimated the beta of a stock at 0.8, with a z-statistic of 1.7 in a sample size of 300 observations. At 5% significance level in a two-sided test the critical value is 1.96, therefore, the manager should conclude that:
Answer(s): A
Since the z-statistic is less than the critical value of 1.96 in a two-sided test, the null hypothesis that beta = 0 cannot be rejected. Note, however, that this does not imply that beta equals zero. It just says that with the given observations, one cannot conclude that beta is statistically significantly different from zero. This is always the interpretation of the null hypothesis (that's the reason statisticians emphasize that "failing to reject the null hypothesis" is not the same as "accepting the null hypothesis." You should always remember this.) Also note that the nature of the alternative hypothesis is important. If the alternative had been onesided (beta > 0), then the null would be rejected in this case at the 5% level.
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