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A random sample of 140 egg lovers is asked to state their gender and egg preference. The results are recorded in the table.

Gender Fried Poached Scrambled Boiled
Male 22 21 16 18
Female 25 13 21 4

A chi-square test is used to test the null hypothesis that gender and egg preference are independent. Which of the following statements is correct?

Fail to reject H0 at the 0.3 significance level.

Fail to reject H0 at the 0.1 significance level.

Reject H0 at the 0.01 significance level.

Reject H0 at the 0.005 significance level.

Fail to reject H0 at the 0.01 significance level.

User Eric Genet
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Final answer:

To test the null hypothesis that gender and egg preference are independent, we can use a chi-square test of independence. The correct statement is: Reject H0 at the 0.01 significance level.

Step-by-step explanation:

To test the null hypothesis that gender and egg preference are independent, we can use a chi-square test of independence. First, we need to calculate the expected frequencies for each cell in the table under the assumption of independence. These can be found by multiplying the row and column totals and dividing by the total sample size. Once we have the expected frequencies, we can calculate the chi-square statistic by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies. Finally, we compare the calculated chi-square statistic to a critical value from the chi-square distribution table, using the appropriate significance level and degrees of freedom. In this case, with 1 degree of freedom, we find that the chi-square statistic is greater than the critical value at the 0.01 and 0.005 significance levels, but not at the 0.3 or 0.1 significance levels. Therefore, the correct statement is: Reject H0 at the 0.01 significance level.

User Red Virus
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