Question

​It's not often that taxes are​ popular, but when a research company recently surveyed 1015 adults in a certain​ area, it found 55​% in favour of a carbon tax. At​ $25/tonne of​ carbon, the tax adds only 5 cents to the price of a litre of gasoline. Complete parts​ a) and​ b) below.

​a) Calculate a 95​%confidence interval for the percentage of adults in favour of the carbon tax and interpret the meaning of your interval in words. Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice.

A.The 95​% confidence interval is between ---------​% and -------​%.​(Round to one decimal place as needed. Use ascending​ order.)

B. The interval should not be calculated because the assumptions and conditions are not met and cannot be reasonably assumed to be met.

Interpret the meaning of the interval in words. Select the correct choice below​ and, if​ necessary, fill in the answer​ box(es) within your choice.

A.It can be stated with 95​% confidence that between -------​% and -------% of adults are in favour of the tax. (Round to one decimal place as needed. Use ascending​ order.)

B.Between -------% and ----------​% of adults are in favour of the tax. ​(Round to one decimal place as needed. Use ascending​ order.)

C.It is probably true that between ------​% and -------​% of adults are in favour of the tax. ​(Round to one decimal place as needed. Use ascending​ order.)

D.It can be stated with 95​% confidence that -------​% of adults are in favour of the tax.​(Round to one decimal place as​ needed.)

E. The interval should not be calculated because the assumptions and conditions are not met and cannot be reasonably assumed to be met.

​b) Phrase your confidence interval in the form commonly used by the​ media, for​ example, "x percent of adults support the X political party. This result is accurate to plus or minus​ y%, n times out of​ N." Select the correct choice below​ and, if​ necessary, fill in the answer boxes within your choice.

A. -------​% of adults are in favour of the tax. This result is accurate to plus or minus --------​%, ---------- times out of 20. ​(Round to one decimal place as​ needed.)

B. The interval should not be calculated because the assumptions and conditions are not met and cannot be reasonably assumed to be met.

​c) How many adults in the area would the company need to survey in order to reduce the width of this confidence interval by 25​%? The number of adults surveyed would need to be at least --------.​(Round up to the nearest whole number as​ needed.)

​d) How much wider is the 99​% confidence interval than the 95​% confidence interval you calculated in​ (a)? Give your answer as the ratio between the widths of the two confidence intervals.

The 99​% confidence interval is ------ times wider than the 95​% confidence interval. ​(Round to three decimal places as​ needed.)

Answer 1