# Chi-Square Test: Phone Service Providers

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In a survey about satisfaction with local phone service, those respondents who rated their current service as excellent and those who rated it Poor-Very Poor were asked to classify their current local service provider. The results are given in the table below:

Type of Company

Current Service Source........Long Distance.... Local Phone.......Power........Cable TV........Cellular Phone

Excellent.....................................264.....................444..................131..............215.....................198

Poor-Very Poor.........................1394....................1318................485...............431.....................572

a) Set up the hypotheses to test whether the proportion of people who rated their company as excellent is the same for each type of company.

b) Calculate the overall proportion of people who rate their current phone service as excellent.

c) Find the expected frequency for each cell and calculate the chi-square test statistic.

d) If you wanted to perform the test at the 0.05 level of significance, what would the critical value of the test be?

e) At the 0.05 level of significance, is there a difference in the proportion of people who rate their local phone service as excellent among the different types of companies?

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##### Solution Summary

This solution provides a detailed, step by step response which illustrates how to compute the required Chi-square test values and analyze the results. A Word document is attached and contains the answers for parts a) to c) (But is most important for parts b) and c)).

##### Solution Preview

a) Set up the hypotheses to test whether the proportion of people who rated their company as excellent is the same for each type of company.

Ho: The proportion of people who rated their company as excellent is the same for each type of company.

Ha: The ...

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