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# Analysis of Qualitative Data

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A). Based on the data, do you think that the respondents are uniformly distributed over the age categories?

b). Set up the hypotheses to test whether the data are uniformly distributed over the age categories.

c). Find the expected frequency distribution and perform the chi-square goodness of fit test.

d). At the 0.05 level of significance, would you say that the respondents were uniformly distributed over the age groups?

##### Solution Summary

Ex. 17.2
As part of a survey on the use of Office Suites Software, the company doing the polling wanted to know whether it's population was uniformly distributed over the following age distribution: under 25, 25 to 44, 45 and up. The company looked at the data it had collected so far and found the following distributions:

Age Group Number of Respondents
Under 25 73
25 to 44 61
45 and up 66
Total 200

a). Based on the data, do you think that the respondents are uniformly distributed over the age categories?

b). Set up the hypotheses to test whether the data are uniformly distributed over the age categories.

c). Find the expected frequency distribution and perform the chi-square goodness of fit test.

d). At the 0.05 level of significance, would you say that the respondents were uniformly distributed over the age groups?

##### Solution Preview

a) Chi-square test(X2) = Sum all cells (Oij-Eij)2/Eij
<br>Degrees of freedom (df) = (r-1)
<br>
<br>There is only one column of data in this question so df is (r-1) not (r-1)(c-1)
<br>The expected frequencies are Eij
<br>The observed frequencies are Oij
<br>
<br>Eij = [Marginal total i x marginal total j]/N
<br>N = 200
<br>As ...

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