Question

An economist reports that 700 out of a sample of 2,800 middle-income American households actively participate in the stock market.Use Table 1.

  

a.	Construct the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stock market. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.)

  

Confidence interval

to

  

b.

Can we conclude that the proportion of middle-income Americans who actively participate in the stock market is not 28%?

	Yes, since the confidence interval contains the value 0.28.
	Yes, since the confidence interval does not contain the value 0.28.
	No, since the confidence interval contains the value 0.28.
	No, since the confidence interval does not contain the value 0.28.

Answer 1

a) = 700/2800 = 0.25

At 90% confidence interval the critical value is z_0.05 = 1.645

+/- z_0.05 * sqrt((1 - )/n)

= 0.25 +/- 1.645 * sqrt(0.25 * 0.75/2800)

= 0.25 +/- 0.0135

= 0.2365, 0.2635

b) Option - B) Yes, since the confidence interval does not cointain the value 0.28.