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According to a recent survey, 85% of stocks in the U.S. market are held by institutional...

According to a recent survey, 85% of stocks in the U.S. market are held by institutional investors.

a. Suppose that the survey had a sample size of n=1000. Construct a 95% confidence interval for the proportion of all U.S. stocks held by institutional investors.

b. Based on (a), can claim that more than 80% of U.S. stocks are held by institutional investors?

c. Discuss the effect of sample size on confidence interval

Math   Statistics-And-Probability   
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Answer #1

we have p = 0.85 and n = 1000

(A) using the confidence interval formula

CI =

setting the value p = 0.85, n = 1000 and z = 1.96 for 95% confidence interval using normal distribution table.

we get

CI =

this gives

CI =

so, we are 95% confident that the 82.79% to 87.21% of US stocks are held by institutional investors.

(B) No, we are not able to support the claim that 80% of US stocks are held by institutional investors because the 95% confidence interval does not include 0.80.

(C) The sample size is invesely related to the confidence interval because when we increase the sample size, the confidence interval width decreases and when we decrease the sample size, then the confidence interval width increases.

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