12 select the best response a How much do you plan to spend

12. , select the best response.

(a) How much do you plan to spend for gifts this holiday season? An interviewer asks this question of 250 customers at a large shopping mall. The distribution of individual responses is skewed, but the sample mean and standard deviation of the responses are x = 437 dollars and s = 65 dollars.

Which of the following are true?

A. The margin of error for a 95% confidence interval will be less than the margin of error for a 99% confidence interval.

B. If we calculate a confidence interval, it cannot be trusted since the sample responses may be badly biased.

C. The Central Limit Theorem informs us that we can act as if x is approximately Normally distributed.

D. All of the above.  

(b) A Gallup Poll asked the question How would you rate the overall quality of the environment in this country today - as excellent, good, only fair, or poor? In all, 46% of the sample rated the environment as good or excellent. Gallup announced the poll’s margin of error for 95% confidence as ±3 percentage points. Which of the following sources of error are included in the margin of error?

A. Nonresponse - some people whose numbers were chosen never answered the phone in several calls or answered but refused to participate in the poll.

B. The poll dialed telephone numbers at random and so missed all people without phones.

C. There is chance variation in the random selection of telephone numbers.

D. All of the above.  

Solution

12.

OPTION D: All of the above. [ANSWER]

Larger confidence levels are wider confidence intervals.

As it is a large shopping mall, the sample there may not be a good representative of the population.

The central limit theorem lets us to treat Xbar as normally distirbuted.

Hence, all of the above.

*************************

13.

OPTION C: There is a chance in variation in the random selection of telephone numbers. [ANSWER]

Biases such as nonresponse and not contacting those without telephones are not taken into account when doing a confidence interval.