Question

It's not often that taxes are​ popular, but when a research company recently surveyed 1037 adults, 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 an 80​% 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 80​% 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.

2) Phrase your confidence interval in the form of 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."

a) ___% of adults are in favour of the tax. This result is accutate to plus or minus ___%. ___ times out of 20.

b) the interval should not be calculated because the assumptions and conditions are not met and cannot be reasonably assumed to be met

Answer 1

n=1037 is the sample size

is the sample proportion of adults in favor of carbon tax

The value of

are both greater than 5. Hence we can use normal approximation for the distribution of proportion.

The standard error of the proportion is

We need the critical value of z for 80% confidence interval.

The significance level for 80% confidence interval is

This means the total area under 2 tails is 0.20. The area under the right tail is 0.10.

the critical value is

Using the standard normal tables, for x=1.28, we get P(Z<1.28)=0.5+0.3997=0.8997

Hence the critical value is

The margin of error is

The 80% confidence interval is

ans:  A.The 80​% confidence interval is between 53.0% and 57.0%.

2)  80% confidence interval indicates that the interval is going to contain the true proportion 20*0.8=16 times out of 20  

We need to specify : This result is accurate to plus or minus (Margin of Error)%, 16 times out of 20." The margin of error is 0.0198 or 2%

ans: a) 55% of adults are in favour of the tax. This result is accurate to plus or minus 2%. 16 times out of 20.