In Question 2, Fred constructed a 95% confidence interval to estimate the averag

Question

In Question 2, Fred constructed a 95% confidence interval to estimate the average length (in minutes) of the movies he watches, with a random sample of 15 movies. He plans to continue collecting data until he has a random sample of 40 movies, and then create a new confidence interval. Which of these statements is most accurate?. A) Both the standard error of the mean and the critical value will probably decrease for the larger sample. B) The critical value will increase for the larger sample, but the standard error will probably decrease. C) Since 40 is a large sample, he will be able to use the Normal distribution. D) With this larger sample he can be more sure that his 95% confidence interval captures the true mean length of all movies he watches.

Explanation / Answer

Standard error is inversely related to number of observations in the samplpe. So for large values SE decreases

and also critical value decreases as SE decreases, since by the formula we have length of critical value directly prroportional to Standard errror . hence option A is the correct answer

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