Working for an interior decorator you are involved in a discussion involving the color of trim that is desired by your customers. You suggest that the following distribution of colors is what the market wants: 15% prefers red; 20% prefers blue; 10% prefers yellow; 30% prefers purple; 25% prefers turquoise. Your manager doesn’t agree with your color distribution so she takes a random sample of 200 customers in your market. The following results and table emerges. Colors Your Suggested Percentages Frequencies Preferred in the Sample Red 15% 36 Blue 20% 24 Yellow 10% 30 Purple 30% 66 Turquoise 25% 44 Totals 100% 200 Set up hypotheses and perform the appropriate test to determine if the data reasonably conform to your suggested distribution of color preferences. Discuss the results of your findings and state your conclusion.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Working for an interior decorator you are involved in a discussion involving the color of trim that is desired by your customers. You suggest that the following distribution of colors is what the market wants: 15% prefers red; 20% prefers blue; 10% prefers yellow; 30% prefers purple; 25% prefers turquoise. Your manager doesn’t agree with your color distribution so she takes a random sample of 200 customers in your market. The following results and table emerges.
Colors Your Suggested Percentages Frequencies Preferred in the Sample
Red 15% 36
Blue 20% 24
Yellow 10% 30
Purple 30% 66
Turquoise 25% 44
Totals 100% 200
Set up hypotheses and perform the appropriate test to determine if the data reasonably conform to your suggested distribution of color preferences.
Discuss the results of your findings and state your conclusion.
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