A researcher wants to be sure that the sample in her study is not unrepresentative of...

A researcher wants to be sure that the sample in her study is not unrepresentative of the distribution of ethnic groups in her community. Her sample includes 450 European-Americans, 70 African-Americans, 55 Latinos, 32 Asian-Americans, and 150 people without any ethnicity designated. According to census records, her community population is 48% European-American, 12% African-American, 18% Latino, 9% Asian-American, and 13% people without any ethnicity designated. Is her sample unrepresentative of her community? Carry out the steps of hypothesis testing using a chi-square test for goodness of fit at the 0.05 significance level. Explain your answer to a person who has never taken a course in statistics.

Solutions

Expert Solution

450+70+55+32+150 = 757 = N (total sample size)

Therefore the observed sample proportion for each category of ethnicity are():
0.594451
0.0924702
0.072655217
0.042272126
0.198150594

And the expected proportion are(the population proportions)():
0.48
0.12
0.18
0.09
0.13

We are going to compute the chi-square statistic using the formula:

The above was the result found. Hence as p is so low i.e p<0.05, our significance level, therefore, we reject the hypothesis that her sample is representing her community.

In layman terms her sample is unrepresentative of her community. The sample seems biased and not from her community..

Thank You. Do leave a thumbs up if this helps.

orchestra answered 1 year ago

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