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# Comparisons Involving Proportions

One of the questions on a 2004 Business Week Survey was 'when making investment purchases, do you use full service or discount brokerage firms?'. Survey results, which is based on the indication of preference from 1000 respondents, showed that 28.4% of the respondents used only full services and discount brokerage firms. Use alpha= 0.10 significance level to determine whether there are any differences in preference among the three service choices. In other words, you want to test whether the proportions of people selecting the three services are about the same or not. The null hypothesis is: Ho= Pfull = Pdisc = Pboth.

See table in attachment, see attached file for better formula.

#### Solution Preview

See attachment for solution.

We use chi squared test to test the above H0; We can set up the following table.

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#### Solution Summary

This solution contains step-by-step calculations to determine the p-value using observed frequency and expected frequency, and finally decides to reject or accept the null hypothesis.

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