In: Statistics and Probability
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)
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.
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