The Chi-Square Goodness-of-Fit-Test
This problem looks at the data for the black-sounding female names in the study on racial and sexual employment discrimination described in Chapter 22. Previously we did a 2 sample z test to check whether there was racial discrimination in interview request rates.
Now we'll dochi sq testto see if employers favor some black-sounding female names over others.
The Observed column below gives how many interview requests were given to each name. Remember all resumes were identical except for the names. The question is whether the differences in the number receiving interviews among the names was just due to chance (null) or whether it reflected real name discrimination. In other words, do employers favor some names over others?
The null hypothesis is that there is no name discrimination. Under the null hypothesis, how many interview requests would you expect for each name? Fill in the blanks of the table below.
(Hint: Look at the astrological example in the Chapter 23 part 1 of the Notebook. It's the same type of problem.)
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What is the chi-square statistic? (Note: Since the expected is the same for each name, you have a common denominator so you can divide the sum you just computed by the common expected.)
How many degrees of freedom?
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The significance level P, is closest to
0% .5% 2% 5% 8% 10%
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What do you conclude?
Cannot reject the null; it's plausible that there is no name discrimination. Reject the null, there is strong evidence of name discrimination.
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