# Comparisons Involving Proportions

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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.

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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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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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###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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