Daily gross sales (in thousands of dollars) were recorded for a sample of 20 small businesses in the New York metropolitan area in March 2009, yielding a mean of 283.2 with a standard deviation of 118.023. Suppose the daily gross sales for all small businesses follow a normal distribution. (A) Find a 95% confidence interval for the true mean daily gross sales for all small businesses. (B) Interpret the confidence interval in the context of the problem. What does "95%" mean? (C) What is the margin of error of the interval?
Daily gross sales (in thousands of dollars) were recorded for a sample of 20 small businesses in the New York metropolitan area in March 2009, yielding a mean of 283.2 with a standard deviation of 118.023. Suppose the daily gross sales for all small businesses follow a normal distribution. (A) Find a 95% confidence interval for the true mean daily gross sales for all small businesses. (B) Interpret the confidence interval in the context of the problem. What does "95%" mean? (C) What is the margin of error of the interval?
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Transcribed Image Text:3. Daily gross sales (in thousands of dollars) were recorded for a sample of 20 small businesses in the
New York metropolitan area in March 2009, yielding a mean of 283.2 with a standard deviation of
118.023. Suppose the daily gross sales for all small businesses follow a normal distribution.
(A) Find a 95% confidence interval for the true mean daily gross sales for all small businesses.
(B) Interpret the confidence interval in the context of the problem. What does "95%" mean?
(C) What is the margin of error of the interval?
(D) Based on the confidence interval, do you believe the claim that the true mean daily gross sales is
200 thousand dollars? Explain.
(E) Would a smaller margin of error result from a smaller or larger confidence level?
(F) Suppose the population standard deviation were known to be 120.
(i) Find a 95% confidence interval for the true mean daily gross sales for all small businesses.
(ii) How many small businesses should be sampled to obtain a 99% confidence level with the
same interval width?
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