An economist reports that 300 out of a sample of 1,000 middle-income American ho
ID: 3134708 • Letter: A
Question
An economist reports that 300 out of a sample of 1,000 middle-income American households actively participate in the stock market.Use Table 1.
a. Construct an 95% confidence interval for the proportion of middle-income Americans who actively participate in the stock market. (Round intermediate calculations to 4 decimal places, "z" value to 2 decimal places, and final answers to 3 decimal places.)
Can we conclude that the proportion of middle-income Americans who actively participate in the stock market is not 35%?
b.Can we conclude that the proportion of middle-income Americans who actively participate in the stock market is not 35%?
1. Yes, since the confidence interval contains the value 0.35. 2. Yes, since the confidence interval does not contain the value 0.35. 3. No, since the confidence interval contains the value 0.35. 4. No, since the confidence interval does not contain the value 0.35.Explanation / Answer
A)
Note that
p^ = point estimate of the population proportion = x / n = 0.3
Also, we get the standard error of p, sp:
sp = sqrt[p^ (1 - p^) / n] = 0.014491377
Now, for the critical z,
alpha/2 = 0.025
Thus, z(alpha/2) = 1.96
Thus,
Margin of error = z(alpha/2)*sp = 0.028403098
lower bound = p^ - z(alpha/2) * sp = 0.271596902
upper bound = p^ + z(alpha/2) * sp = 0.328403098
Thus, the confidence interval is
( 0.271596902 , 0.328403098 ) [ANSWER]
*********************
b)
As we can see, 0.35 is not inside this interval, so
OPTION 2: Yes, since the confidence interval does not contain the value 0.35. [ANSWER]
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.