Question

1. There is a Facebook group devoted to The Golden Girls. On a regular basis, the group poses the question: Which Golden Girl was your favorite? A recent random sample of members of the Facebook group answered the question, given in the table below.

GG Character	Rose	Sophia	Dorothy	Blanche	I can’t decide!
Frequency	42	73	38	64	53

At the .05 level of significance, is there evidence to show that the distribution of favorite Golden Girls character is not uniform? (meaning, not an equal distribution)

Answer 1

Let fi denote the observed frequency of GG charector and let ei denotes the expected frequency. Since there are total 270 sample size and if we expect that distribution of favorite Golden Girls of all 5 charector is uniform than there will be 270/5=54 frequency each GG charector. Here we have to test if

H0: The distribution of charector is uniform
H1: The distribution of charector is not uniform

To test above hypothesis we use Chi-square test whose test statistic is given by

By using table we calculate value of test statiistc as

At alpha= 0.05 and df=4 the critical value of chi-square is given by

since calculated chisquare is greater than critcal value thus the null hypothesis is rejected. that is, there is significant evidence to show that the distribution of favorite Golden Girls character is not uniform.