Question

# A market researcher believes that brand perception of one of the company's products may vary between...

A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 327persons, the following data was compiled. Can we conclude that brand perception is dependent on age?

Age Favorable Unfavorable Neutral Total
18-30 69 21 25 115
30-45 67 24 22 113
Over 45 56 21 22 99
Total 192 66 69 327

Step 1 of 8: State the null and alternative hypothesis.

Step 2 of 8: Find the expected value for the number of particpants who are 18-30 years old and have a favorable perception of the brand. Round your answer to one decimal place.

Step 3 of 8: Find the expected value for the number of particpants who are 18-30 years old and have a neutral perception of the brand. Round your answer to one decimal place.

Step 4 of 8: Find the value of the test statistic. Round your answer to three decimal places.

Step 5 of 8: Find the degrees of freedom associated with the test statistic for this problem.

Step 6 of 8: Find the critical value of the test at the 0.1 level of significance. Round your answer to three decimal places.

Step 7 of 8: Make the decision to reject or fail to reject the null hypothesis at the 0.1 level of significance.

Step 8 of 8: State the conclusion of the hypothesis test at the 0.1 level of significance.

Step 1 : the null and alternative hypothesis.

H0:  brand perception is independent on age

vs

H1: brand perception is dependent on age

Step 2 : the expected value for the number of particpants who are 18-30 years old and have a favorable perception of the brand=67.5

Step 3 : the expected value for the number of particpants who are 18-30 years old and have a neutral perception of the brand=24.3

Step 4 : the value of the test statistic=0.665

Step 5 : the degrees of freedom associated with the test statistic for this problem.

=(Row-1)(Column-1) = 2*2 = 4

Step 6 : the critical value of the test at the 0.1 level of significance=7.779

Step 7 : fail to reject the null hypothesis at the 0.1 level of significance.

Since P value 0.9555 > 0.10

Step 8 : There is not enough evidence to say that, brand perception is dependent on age

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