W4002- Please help me with this stats question! (dealing with confidence interval and sample size)?

Set up a 95% confidence interval estimate of the population average number of shares traded for......?


The following table is a random sample of 18 stocks traded on the New York Stock Exchange as reported in the Cincinnati Enquirer (May 18, 1999). For each stock, the table lists the company name and the number of shares that traded hands on May 17, 1999.





CompanyShares


AllenTel408700


Banctec29500


CDI32500


CTS36700


Dover169100


Fluor332000


Grace237700


Hartmx49700


KCS110300


LizClab219400


NuvPP50700


Presly133500


StJude163500


Scripps27900


SunEng63400


Thai67200


Tyson161800


YorkIn120000





(a) Set up a 95% confidence interval estimate of the population average number of shares traded for a company on the New York Stock Exchange on May 17, 1999.





(b) What sample size is needed if you want to be 95% confident of being correct to within :t:20,000 shares?





(c) If you were to perform this study today, do you think that your answer to (b) is valid? Explain.





THANKS!

W4002- Please help me with this stats question! (dealing with confidence interval and sample size)?
(a)


Sum = 2413600


n = 18


Average = 134088.8889


Standard deviation = 108947.5907





Lower confidence limit: 134088.9 - 1.96*108947.6/√18


Upper confidence limit: 134088.9 + 1.96*108947.6/√18





The 95% confidence interval is (83757.67, 184420.10)


or (83757, 184421) conservatively





(b)


20000 / [(108947.5907)/√n ] = 1.96


20000 * (√n) / (108947.5907) = 1.96


√n = (1.96/20000)*108947.5907 = 10.6768639


n = 113.995422.





A sample size of 114 would be the minumum number of samples to be 95% confident of being correct to within :t:20,000 shares.





(c)


The confidence interval in (b) is based on the variation seen in 1999. If the variation is statistically the same then 114 samples are sufficient. You would need to test this, if the variation is not similiar then the calculation needs to be redone by substituting in the value of the standard deviation.

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