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

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, p_i = 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.

orchestra answered 1 year ago

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