Premium Product Promotions, a market research firm, is trying to determine if there are differences in the brand of beer preferred by various customer groups. Formulate and test a hypothesis for them using a = 0.05 if the following data are the preferences of a sample of 800
CUSTOMER GROUP BRAND OF BEER
Pale Golden Heavy
Housewives 75 20 5
Businessmen 50 130 20
Factory Workers 5 25 170
College Students 100 100 100
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To test whether there are differences in the brand of beer preferred by various customer groups, we can conduct a chi-squared test of independence. This test will help determine if the preferences for different brands of beer are independent of the customer groups.
Null Hypothesis (H0): The preference for different brands of beer is independent of the customer groups.
Alternative Hypothesis (H1): The preference for different brands of beer is dependent on the customer groups.
To conduct the chi-squared test, we need to calculate the expected frequencies under the assumption that the null hypothesis is true. We can use the formula:
Expected Frequency = (row total * column total) / total sample size
First, let's calculate the observed frequencies:
CUSTOMER GROUP BRAND OF BEER Observed Frequency
Housewives Pale 75
Housewives Golden 20
Housewives Heavy 5
Businessmen Pale 50
Businessmen Golden 130
Businessmen Heavy 20
Factory Workers Pale 5
Factory Workers Golden 25
Factory Workers Heavy 170
College Students Pale 100
College Students Golden 100
College Students Heavy 100
Now let's calculate the expected frequencies:
CUSTOMER GROUP BRAND OF BEER Observed Frequency Expected Frequency
Housewives Pale 75 [(75+20+5)*(75+50+5+100)] / 800
Housewives Golden 20 [(75+20+5)*(20+130+5+100)] / 800
Housewives Heavy 5 [(75+20+5)*(5+20+5+100)] / 800
Businessmen Pale 50 [(50+130+20)*(75+50+5+100)] / 800
Businessmen Golden 130 [(50+130+20)*(20+130+5+100)] / 800
Businessmen Heavy 20 [(50+130+20)*(5+20+5+100)] / 800
Factory Workers Pale 5 [(5+25+170)*(75+50+5+100)] / 800
Factory Workers Golden 25 [(5+25+170)*(20+130+5+100)] / 800
Factory Workers Heavy 170 [(5+25+170)*(5+20+5+100)] / 800
College Students Pale 100 [(100+100+100)*(75+50+5+100)] / 800
College Students Golden 100 [(100+100+100)*(20+130+5+100)] / 800
College Students Heavy 100 [(100+100+100)*(5+20+5+100)] / 800
Once we calculate the expected frequencies, we can perform the chi-squared test to determine if the observed frequencies significantly differ from the expected frequencies.
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