Question

8. There are four candidates for a job, Elaine, Jazmine, Jamal, and Matt. The firm believes all candidates are equally well-liked by the people that met them. 150 people met the candidates; 30 preferred Elaine, 45 Jazmine, 40 Jamal, and 35 Matt.
(a) Write down an appropriate null and alternative hypothesis.

(b) Construct a Chi-square test statistic and test your hypothesis at all levels.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: All candidates are equally well-liked by the people that met them

Alternative hypothesis: At least one of the proportions in the null hypothesis is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05, 0.05, 0.01. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 5 - 1
D.F = 4
(E_i) = n * p_i

X² = 170.833

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 4 degrees of freedom is more extreme than 170.833.

We use the Chi-Square Distribution Calculator to find P(X² > 170.8333) = 0.000

Interpret results. Since the P-value (0.000) is less than the significance level (0.10, 0.05, 0.01), we cannot accept the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that all candidates are equally well-liked by the people that met them.