A researcher obtains z = 3.00 for a binomial test.If a chi-square test for goodness of fit had been used instead of the binomial test,what value would be obtained for chi-square?
A)3
B)6
C)9
D)1/3

Question

A researcher obtains z = 3.00 for a binomial test.If a chi-square test for goodness of fit had been used instead of the binomial test,what value would be obtained for chi-square?​
A)​3
B)​6
C)​9
D)​1/3

Quizplus · Accepted Answer

When a binomial test is used to test a hypothesis about a population proportion, it can be converted to a test of goodness of fit with a chi-square test.

The chi-square statistic for this test is calculated as:

χ2 = ∑ (O - E)2 / E

where O is the observed number of successes, E is the expected number of successes (calculated as the sample size times the hypothesized proportion), and the sum is taken over all possible outcomes.

For a two-tailed binomial test at α = 0.05, the critical value of z is ±1.96. A z-score of 3.00 is beyond the critical value, so we reject the null hypothesis of p = 0.50 (assuming a two-tailed test) in favor of the alternative hypothesis.

To convert to a chi-square test, we first calculate the expected number of successes as E = np = 0.50 x 100 = 50. The observed number of successes is O = 53 (assuming a one-tailed test).

χ2 = (53-50)2/50 + (47-50)2/50 = 3 + 3 = 6.

Therefore, the value obtained for chi-square would be 6.

A Researcher Obtains Z = 3