Question

In March 2012, students in class were surveyed for favorite juice flavor. They were asked to try all four and chose the one they liked the best. Is one type of juice flavor preferred more?

                              # Best Flavor Votes

grape                   15

orange                 6

apple                    15

lemonade            25

1. decide what would be the appropriate statistical test from the list below

1 variable: Chi Square Goodness of Fit Test

2. write out the main question and then the null and alternative hypotheses, defining symbols and making inference to the population

I just need help with part b

Answer 1

Assuming level of significance to be 5%.

Chi-Square Goodness of Fit test

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: H0: p1 =0.25, p2 =0.25, p3​=0.25, p4​=0.25 Ha​: Some of the population proportions differ from the values stated in the null hypothesis This corresponds to a Chi-Square test for Goodness of Fit. (2) Degrees of Freedom The number of degrees of freedom is df=n-1=4-1=3 (3) Test Statistics The Chi-Squared statistic is computed as follows: (4)Critical Value and Rejection Region Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=n-1=4-1=3, so the critical value becomes 7.8147. Then the rejection region for this test is R={χ2:χ2>7.8147}. (5)P-value The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 7.8147. The p-value is p=Pr(χ2>11.8525)=0.0079 (6) The decision about the null hypothesis Since it is observed that χ2=11.8525>χ2_crit​=7.8147, it is then concluded that the null hypothesis is rejected. (7) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.

Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!