Question

Exercise (Milk Preference)

Suppose that customers can purchase one of three brands of milk at a supermarket. In a study to determine whether one brand is preferred over another, a record is made of a sample of n = 300 milk purchases. The data are shown in the following table. Do the data provide sufficient evidence to indicate a preference for one or more brands? Assume α = 5%.

Question 1 2 pts Step 1: Write down your null and alternative hypotheses. Use p1 to represent the proportion of the population who preferred Brand 1 over the other two brands, and p2 to represent the population proportion for Brand 2 and p3 for Brand 3 Ho Null: There is no brand preference, that is p1-p2 p3-1/3: Altemative: there is a preference for one or more brands, that is p's arc not all cqual 。Null: There is a preference tor one or more brands. that is p's are not 28 cqual. Alternative: There is no brand preference, tat is pl-p2-p3-1/3; Null: brand prcference, that is p's are not all cqual Alternative: There is a preferencc for one or more brands, that is pl p2 p3-1/3 O Null: There i5 preference for one or more brands. that is pl . p2·p3·1/3: Alternative. There is no brand preference, tet i5 p's are not all equal There is no Complete the following table based on your hypotheses: Frequency Expected Frequency Brand - fe)2/fe 78 105 Test statistic: Tota300 Step 2 Find the test statistic. Is this a z-score, t-score or chi-square statistic? Find the corresponding degrees of freedom.

What is the value of the test statistic?

What are the degrees of freedom?

What is the p value?

Given the significance level, a = 5%, what’s your final conclusion? Would you conclude that there is preference for one or more brands?

Answer 1

sl Conside tfe 히 ocong given data So, cosmet op ion s D. obsenad ERected chi seuare Oi 2.000 131O00 o5 ooo 200 1.8 2.29 (0ovo 00 O 300 7920 value of the test gtatisti s7 30 SIcP3: p-value =0, 이 25 H10othesis and conclhde tha these s peferena