Question

An owner of a candy shop would like to know which of their products her customers prefer over others. The owner conducts a customer preference survey based on a sample of 1150 customers. The results are given in the table below. Conduct the appropriate hypothesis test using an alpha level of .01. Chocolate Covered Cherries Gummy Ropes Jawbreakers Sugar-Free Gum 320 265 285 280 4A. Set up the criteria for making the decision. That is, find the critical value. (1 point) 4B. Summarize the data into the appropriate test-statistic. (3 points) 4C. Evaluate the null hypothesis (circle one) REJECT FAIL TO REJECT (1 point)

Answer 1

Solution:-

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

Null hypothesis: There is preference for particular products on her candy shop.

Alternative hypothesis: There is no preference for particular products on her candy shop.

Formulate an analysis plan. For this analysis, the significance level is 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 = 4 - 1
D.F = 3
(E_i) = n * p_i

X² = 5.652

X²_Critical = 11.35

Rejection region is X² > 11.35

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.

Interpret results. Since the X² -value (5.652) does not lies in the rejection region, hence we cannot reject the null hypothesis.

FAIL TO REJECT Null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that her costumers don't have any preference in the products.