Question

A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 401persons, the following data was compiled. Can we conclude that brand perception is dependent on age?

Age	Favorable	Unfavorable	Neutral	Total
18-30	66	16	16	98
30-45	70	42	42	154
Over 45	98	24	27	149
Total	234	82	85	401

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 30-45 years old and have a favorable 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.

Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

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

  State the conclusion of the hypothesis test at the 0.05 level of significance.

There is significant evidence that brand perception and age are related.

or

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

Answer 1

a). hypothesis:-

brand perception and age are independent.

brand perception and age are not independent.

the expected frequency table be:-

age	favorable	unfavorable	neutral
18-30	(98*234)/401= 57.19	(98*82)/401= 20.04	(98*85)/401= 20.77
30-45	(154*234)/401= 89.87	(154*82)/401= 31.49	(154*85)/401= 32.64
over 45	(149*234)/401= 86.95	(149*82)/401=30.47	(149*85)/401= 31.58

step 2:-

the expected value for the number of participants who are 18-30 years old and have a favorable perception of the brand = 57.2

step 3:-

the expected value for the number of participants who are 30-45 years old and have a favorable perception of the brand = 89.9

step 4 :-

the test statistic be:-

= 17.293

step 5 :-

the degrees of freedom associated with the test statistic for this problem = (3-1)*(3-1) = 4

step 6:-

the critical value of the test at the 0.1 level of significance = 7.779

[ from chi square distribution table, for df = 4 , alpha= 0.1 ]

the critical value of the test at the 0.05 level of significance = 9.488

[ from chi square distribution table, for df = 4 , alpha= 0.05 ]

step 7 :-

so, we reject the null hypothesis at 0.1 level of significance.

so, we reject the null hypothesis at 0.05 level of significance.

step 8:-

the conclusion of the hypothesis test at the 0.1 level of significance be:-

There is significant evidence that brand perception and age are related.

the conclusion of the hypothesis test at the 0.05 level of significance be:-

There is significant evidence that brand perception and age are related.

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