The correct answer for this is D. On a T-distribution we are not guaranteed that 95% of the area will fall within 2 standard deviations of the mean, even though this is a fact for the normal distribution. This isn't proof for a T-distribution. Especially for when we have a small number of observations. The answer is true, because the researchers measured what really the entire population we can safely say that this is a true value and there is no sample statistic involved. The correct answer is b. the standard is a measure of variability of the sample statistic. A is incorrect because the formula given in a is valid only for the standard area for mean. But we could have standard errors of a lot of other statistics as well. For example, we could have standard errors for mo-modes and medians, and the formula for that would not be the formula given in it. Meanwhile, we know that the formula for the Standard Error in a mean is the standard deviation divided by the square root of the number of observations. In this case our standard deviation is 10. We have 400 observations, we see that the standard data comes out to be 0.5. The correct answer for this question is B. The size of the smallest group, and we can illustrate that using a very simple example. Let's say we have a case where a was 1, b was 10, c was 100 and d was 1,000. We can see that of all expressions in the formula come out to be one by one plus .1 plus .01 plus .001. And we can see that the first expression is the one that are going to impact the standard error the most. The correct answer here is d. Different statistics have different forcumlas for standard errors. We know that the formula for standard error of the mean. It is given by the standard deviation divided by the square root of the number of observations, but this is only the formula for the standard error of the mean. We have very different formulas for the standard errors or the mean, the modes, the median for example. The answer to this question is d, all of the above. The confidence interval gives us information about the effect size, the precision and the statistical significance. The correct answer is a, changing from a 99 to a 95% confidence level. Because [INAUDIBLE] lower level of Confidence decreases the rate of of the confidence interval. A 95% confidence interval of a mean will include the true population mean 95% of the time. This is true by the definition of the confidence interval. If we sample both women and men together we would have a higher standard deviation of heights because we would expect the men to be taller than the women, is the only sample of women we would expect the heights to be closer together, because of which the standard deviation would be lower. The first confidence interval would be narrow, narrower because it involved a larger sample size. We know that the formula for the margin of error is, one by the square root of the number of observations, which comes out to 4%. In this case, we know that the mean is 55%. In the previous question, we calculated that when we have 625 observations, the margin of error is 4%. So if we want to find the lower and upper bound for a 95% interval, this would be 55% plus or minus 4%. The lower bound would be 55% minus 4%, which is 51. And the upper bound would be 55% plus 4%, which is 59%. The correct answer is b. Because the smallest standard error will result in a smaller p value. The correct answer here is d. There is not enough evidence to reject the null hypothesis. A is incorrect because we have failed to prove that the treatments differ but this is not equivalent to proving the treatments are the same. B is incorrect because we were not given enough information about whether the drug in the placebo improved the insomnia symptoms. C is incorrect because the high value, P value shows us that we cannot reject the null hypothesis [SOUND]. In this question the correct answer is C. There is only 2% chance that the observed difference in cure rates could have arisen if the drug had no effect. This is by the definition of the B value.