An advertising agency is trying to predict the percent of people who want certain colors of...

An advertising agency is trying to predict the percent of people who want certain colors of nerds. They are claiming that 35% of the people like blue nerds, 45% would like red nerds and 20% would like mixed nerds. A random sample of 500 people revealed that 250 wanted blue, 200 wanted red, and 50 wanted mixed. Does this data suggest that the percentages on which the staffing is correct? Use a level of significance of .05 to test the claim.

Expert Solution

null hypothesis:Ho: Sample distribution of colors is similar to as stated by agency .

Alternate hypothesis:Ha: Sample distribution of colors is different then as stated by agency .

degree of freedom =categories-1=

2

for 2 df and 0.05 level of signifcance critical region χ2=

5.991

Applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	O_i	E_i=total*p	R²_i=(O_i-E_i)/√E_i	R²_i=(O_i-E_i)²/E_i
Blue	0.35	250	175.00	5.67	32.143
red	0.45	200	225.00	-1.67	2.778
Mixed	0.20	50	100.00	-5.00	25.000
total	1.000	500	500		59.921

as test statistic X² =59.921 is in critical region we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that Sample distribution of colors is different then as stated by agency .

orchestra answered 2 years ago

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