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A researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile. Each individual in a sample of n = 30 males and n = 30 females selects a favorite design from the three choices. If the researcher obtains a chi-square statistic of χ2 = 4.81, what is the appropriate statistical decision for the test?

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Answer:

Step-by-step explanation:

Given that a researcher is conducting a chi-square test for independence to evaluate the relationship between gender and preference for three different designs for a new automobile.

Thus we have gender divided into two rows and 3 designs into 3 columns

i.e. [tex]r=2 and c = 3[/tex]

So degree of freedom [tex]= (r-1)(c-1)\\=2[/tex]

Chi square = 4.81

p value = 0.090265

If significance level of 5% is taken then we hae

p value >0.05

Hence accept null hypothesis that there is independence between gender and designs

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