Question

​It's not often that taxes are​ popular, but when a research company recently surveyed 1011 ​adults, it found 57​% 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.

1) Calculate a 90% confidence interval for the percentage of adults in favour of the carbon tax, and interpret the meaning of your interval in words.

a) The 90​% 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

Solution:-

1)

a) The 90​% confidence interval is between 54.44% and 59.56%.

$C.I = \hat{p}\pm z_{\alpha /2}\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

C.I = 0.57 + 1.645*0.0155703

C.I = 0.57 + 0.02561

C.I = ( 0.5444, 0.5956)

C.I = (54.44%, 59.56%)

2) a) 57% of adults are in favour of the tax. This result is accurate to plus or minus 2.56%. 18 times out of 20.