Evalutating Confidence Intervals
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The Statistical Abstract of the United States reports that the mean daily number of shares traded on the NYSE in 2002 was 1441 million. Assume that the population standard deviation equals 500 million shares. Suppose that, in a random sample of 36 days from the present year, the mean daily number of shares traded equals 1.5 billion. Let the confidence level be 95%.
a. Find the point estimate of the population mean.
b. Calculate (sigma)/sqrt(n)
c. Find Z(alpha)/2 for the confidence interval.
d. Compute and interpret the margin of error for the confidence interval.
e. Construct and interpret the confidence interval for the population mean.
f. How large a sample size (trading days) is needed to estimate the population mean number of shares traded per day to within 100 million with 95% confidence?
g. How large a sample size (trading days) is needed to estimate the population mean number of shares traded per day to within 10 million with 95% confidence? How many years does this number translate to?
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Solution Summary
The expert evaluates confidence intervals for statistical abstracts of the United States. Confidence intervals are computed to estimate the population mean numbers of shares traded.
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Confidence Intervals
The Statistical Abstract of the United States reports that the mean daily number of shares traded on the NYSE in 2002 was 1441 million. Assume that the population standard deviation equals 500 million shares. Suppose that, in a random sample of 36 days from the present year, the mean daily number of shares traded equals 1.5 billion. Let the confidence level be 95%.
Answers
a. Find the point estimate of the population mean.
Point estimate of the population mean = 1441 million
b. Calculate (sigma)/sqrt(n)
Here σ = 500, n = 36
Therefore, = 83.33333
c. Find Z(alpha)/2 for the confidence interval.
is obtained from the standard normal table at the significance level, α = 1 - 0.95 = ...
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