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A large department store chain is considering opening a new store in a town of 15,000 people. Before making the decision, a market survey is conducted. Of 200 persons interviewed, 165 indicated they would patronize the new store. Find a 95% confidence interval on the proportion p of people who will patronize the store. Use this to give a 95% confidence interval on the number of people who will patronize the store.

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A large department store chain is considering opening a new store in a town of 15,000 people.  Before making the decision, a market survey is conducted.  Of 200 persons interviewed, 165 indicated they would patronize the new store. Find a 95% confidence interval on the proportion p of people who will patronize the store.  Use this to give a 95% confidence interval on the number of people who will patronize the store.

amistre64 · Answer

do you know the zscore of 95%?

anonymous · Answer

no

amistre64 · Answer

$$\hat p\pm Z_{95}~\sqrt{\frac{pq}{n}}$$

amistre64 · Answer

you have to have a way to determine the zscore for 95% ... what methods are available to you?

anonymous · Answer

The range of the confidence interval is defined by the sample statistic + margin of error. And the uncertainty is denoted by the confidence level.

amistre64 · Answer

$\hat p$ is the fraction of people that liked it:  165 out of 200

the Z is the associated zscore for 95% about the mean

and the rest is really amounts to the square root of:  165 times (200-165), divided by 200^3

amistre64 · Answer

lets assume for the moment that a zscore of 95% is say ... 1.96

amistre64 · Answer

$$\frac{165}{200}\pm1.96\sqrt{\frac{165*35}{200^3}}$$represents our confidence interval

anonymous · Answer

you get the value of 1.96 from the table

anonymous · Answer

thank you very much

amistre64 · Answer

youre welcome