Question

Steps 1-8. thank you.

Save & EXIT Lesson. 10. estion 1 of 3, Step 1 of 8 0/24 Correct market researcher believes that brand perception of one of the company's products may vary between different groups. After interviewing 340 persons, the follo ata was compiled. Can we conclude that brand perception is dependent on age? Favorable Unfavorable Neutral Total Age 18-30 69 14 14 97 54 47 47 148 30-45 Over 45 69 12 14 95 Total 192 73 75 340 Copy Data Step 1 of 8 : State the null and alternative hypothesis, Answer E Tables Екеура Keyboard Shortc Ho: brand perception and age are independent Submit Answer 2020 Hawkes Learning

Answer 1

Observed Frequencies
	Favorable	Unfavorable	Netural	Total
18-30	69	14	14	97
30-45	54	47	47	148
Over 45	69	12	14	95
Total	192	73	75	340
Expected Frequencies
	Favorable	Unfavorable	Netural	Total
18-30	192 * 97 / 340 = 54.7765	73 * 97 / 340 = 20.8265	75 * 97 / 340 = 21.3971	97
30-45	192 * 148 / 340 = 83.5765	73 * 148 / 340 = 31.7765	75 * 148 / 340 = 32.6471	148
Over 45	192 * 95 / 340 = 53.6471	73 * 95 / 340 = 20.3971	75 * 95 / 340 = 20.9559	95
Total	192	73	75	340
	(fo-fe)²/fe
18-30	(69 - 54.7765)²/54.7765 = 3.6934	(14 - 20.8265)²/20.8265 = 2.2376	(14 - 21.3971)²/21.3971 = 2.5572
30-45	(54 - 83.5765)²/83.5765 = 10.4667	(47 - 31.7765)²/31.7765 = 7.2933	(47 - 32.6471)²/32.6471 = 6.3101
Over 45	(69 - 53.6471)²/53.6471 = 4.3938	(12 - 20.3971)²/20.3971 = 3.4569	(14 - 20.9559)²/20.9559 = 2.3089

1)

Null and Alternative hypothesis:

Ho: Brand perception and age are independent.

H1: Brand perception and age are dependent.

2)

E(18-30 and favorable) = 192 * 97 / 340 = 54.8

3)

E(Over 45 and neutral) = 75 * 95 / 340 = 21.0

4)

Test statistic:

χ² = ∑ ((fo-fe)²/fe) = 42.718

5)

df = (r-1)(c-1) = 4

6)

Critical value:

χ²α = CHISQ.INV.RT(0.01, 4) = 13.277

7)

Decision:

Reject the null hypothesis.

8)

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