Question

A market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 269 persons, the following data was compiled. Can we conclude that brand perception is dependent on age?

Age	Favorable	Unfavorable	Neutral	Total
1818-3030	45	8	7	60
3030-4545	54	8	8	70
Over 4545	51	44	44	139
Total	150	60	59	269

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.

Step 8 of 8:

State the conclusion of the hypothesis test at the 0.1 level of significance.

Answer 1

NULL HYPOTHESIS H0: VARIABLES ARE INDEPENDENT

ALTERNATIVE HYPOTHESIS Ha: VARIABLES ARE DEPENDENT

the expected value for the number of particpants who are 18-30 years old and have a favorable perception of the brand is 35.39

the expected value for the number of particpants who are 30-45 years old and have a favorable perception of the brand is 41.34

The value of test statistic= 28.555

degrees of freedom= (3-1)*(3-1)= 2*2= 4

Critical value= 7.779

Decision: REJECT NULL HYPOTHESIS H0 AT 0.1 LEVEL OF SIGNIFICANCE

CONCLUSION: We have sufficient evidence to conclude that the variables are dependent.