A market researcher believes that brand perception of one of the company\'s prod

Question

A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 250 persons, the following data was compiled. Determine at the 0.005 level if brand perception is related to age.

Ho: brand perception and age are dependent

Ha: brand perception and age are independent

Age          Favorable    Unfavorable     Neutral    Total

18-30       48                 10                     8             66

30-45       40                 35                     35           110

Over 45    56                 9                       9             74

Total         144               54                     52           250

Ho: brand perception and age are independent

Ha: brand perception and age are dependent

Find the expected number of observations for the cell corresponding to the row 18-30 and the column Unfavorable. Round to 1 decimal place.

Find the value of the test statistic. Round to 3 decimals.

Find the degrees of freedom associated with the test statistic for the problem.

Find the critical value of the test statistic. Round to 3 decimals.

At the 0.005 level of confidence, determine whether to fail to reject or reject the null hypothesis.

   Fail to reject null Hypothesis                 Reject Null Hypothesis

Choose the correct response at the o.005 lrbrl og dihnigivsnvr.

a. There is significant evidence that brand perception and age we related.

b. There is not significant evidence that brand perception and age are related.

Explanation / Answer

Test statistic = 36.53624 = 36.536

p-value = 0.0000

reject the null hypothesis

a. There is significant evidence that brand perception and age we related.

c1 c2 c3 sum r1 48 10 8 66 r2 40 35 35 110 r3 56 9 9 74 sum 144 54 52 250 Eij 1 2 3 expected 1 38.016 14.256 13.728 2 63.36 23.76 22.88 3 42.624 15.984 15.392 0i 48 10 8 40 35 35 56 9 9 Ei 38.016 14.256 13.728 63.36 23.76 22.88 42.624 15.984 15.392 (Oi-Ei)^2/Ei 2.622061 1.27059 2.390005 8.612525 5.317239 6.42021 4.197574 3.051568 2.654474 sum 36.53624 critical value 9.487729

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