Question

A research company surveyed 1024 adults from one country​ (assume a 50​/50 split between men and​ women) and found that 66% of men and 42​%

of women support scrapping the penny. Let men from this country be population 1 and women from this country be population 2.

1) Construct a 90​% confidence interval for the difference in support for scrapping the penny between men and women.

a)The 90​% 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) Construct a 95​% confidence interval for the difference in support for scrapping the penny between men and women.

a) The 90​% 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.

3) Interpret the meaning of the fact that one of these confidence intervals is wider than the other.

The wider confidence interval provides a) _____ ​coverage, which means that there is a b) _____ probability that it contains the true c)____ value of the estimated difference.

a = More or less

b = greater or lesser

c = population or sample

Answer 1

Solution:

1) Construct a 90 % confidence interval for the difference in support for scrapping the penny between men and women.

Answer: We can use TI-84 to find the 90% confidence interval. The steps are as follows:

Press the STAT key and scroll right to TESTS

Then scroll down to 2-PropZInt...

Input the following information:

$X1=338$ 66% of 512

$n1=512$

$X2=215$ 42% of 512

$n2=512$

$C-level:0.90$

Calculate

The output is given below:

a)The 90 % confidence interval is between 19.1% and 29.0%.

2) Construct a 95 % confidence interval for the difference in support for scrapping the penny between men and women.

Answer: a) The 95 % confidence interval is between 18.1% and 29.9%.

3) Interpret the meaning of the fact that one of these confidence intervals is wider than the other.

Answer: The wider confidence interval provides more coverage, which means that there is a greater probability that it contains the true population value of the estimated difference.