Question

A research company recently surveyed 1043 adults in one country about reform of the​ country's senate. Of​ these, 33% answered​ "Yes" to the question​ "Do you support abolishing the​ senate?" Construct an 80​% confidence interval for this proportion and give a written explanation of what your interval means. 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."

1)Construct an 80% confidence interval for the proportion of all adults in this country who support abolishing the senate. Select the correct choice below​ and, if​necessary, fill in the answer boxes within your choice.

a) The 80% confidence interval is between ___% and ___%.

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 in this country support abolishing the senate. this result is accurate 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 80​% confidence interval is between 31.13% and 34.87%.

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

C.I = 0.33 + 1.282*0.0145597

C.I = 0.33 + 0.01867

C.I = ( 0.3113, 0.3487)

C.I = (31.13%, 34.87%)

2) a) 33% of adults are in favour of the tax. This result is accurate to plus or minus 1.87%. 16 times out of 20.