Question

In: Statistics and Probability

Hair color in the United States is known to be 40% blond, 40% brown, and 20%...

Hair color in the United States is known to be 40% blond, 40% brown, and 20% black. Miranda does a study to see if the proportions match, and her survey showed 43 people with blond hair, 32 people with brown hair, and 15 with black hair. Use a chi-square test with a level of significance α=0.05.

Solutions

Expert Solution

The null and alternate hypothesis are:

H0: Proportions match as required.
Ha: Proportions do not match as required.

Observed (Oi) Expected (Ei)
Blonde 43 0.4(90)=36 1.36
Brown 32 0.4(90)=36 0.44
Black 15 0.2(90)=18 0.50
TOTAL 90 90 2.30

Test statistic value =

The critical value is given by:

Since the test statistic value is less than the critical value, so we do not have sufficient evidence to reject null hypothesis H0. Thus we can say that the proportions match as required.

orchestra answered 2 years ago
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