Question

In: Statistics and Probability

There is a Facebook group devoted to The Golden Girls. On a regular basis, the group...

  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)

Solutions

Expert Solution

hypothesis:-

proportion of all characters are equal,i.e, pi = 1/5 = 0.2

at least one of the character has a different proportion

the necessary calculation table :-

GG character observed expected
rose 42 270*0.2= 54 (42-54)2/54 = 2.66667
sophia 73 54 6.68519
dorothy 38 54 4.74074
blanche 64 54 1.85185
i can't decide 53 54 0.01852
sum =270 sum= 15.96297

the test statistic be:-

df = (5-1) = 4

p value = 0.0031

[ in any blank cell of excel type =CHISQ.DIST.RT(15.96297,4) ]

decision:-

p value = 0.0031 < 0.05 (alpha)

we reject the null hypothesis. There is enough evidence to show that the distribution of favorite Golden Girls character is not uniform.

*** if you have any doubts about the problem please mention it in the comment box... if satisfied please LIKE.


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