Question

A survey was conducted two years ago asking college students their top motivations for using a credit card. To determine whether this distribution has​changed, you randomly select 425 college students and ask each one what the top motivation is for using a credit card. Can you conclude that there has been a change in the claimed or expected​ distribution? Use alpha equals 0.10 .α=0.10. Complete parts​ (a) through​ (d).	Response	Old Survey​%	New Survey ​Frequency, f
	Rewards	2929​%	112112
	Low rates	2323​%	9797
	Cash back	2121​%	109109
	Discounts	88​%	4747
	Other	1919​%	6060

a. State

Upper H 0H0

and

Upper H Subscript aHa

and identify the claim.What is the null​ hypothesis,

Upper H 0H0​?

A.The distribution of motivations is

2929​%

​rewards,

2323​%

low​ rate,

2121​%

cash​ back,

8 %8%

​discounts, and

1919​%

other. Your answer is correct.

B.The distribution of motivations is

112112

​rewards,

9797

low​ rate,

109109

cash​ back,  

4747​discounts,

and

6060

other.

C.

The distribution of motivations differs from the expected distribution.

What is the alternate​ hypothesis,

Upper H Subscript aHa​?

A.

The distribution of motivations is the same as the claimed or expected distribution.

B.The distribution of motivations is

2929​%

​rewards,

2323​%

low​ rate,

2121​%

cash​ back,

8 %8%

​discounts, and

1919​%

other.

C.

The distribution of motivations differs from the claimed or expected distribution.

Your answer is correct.

Which hypothesis is the​ claim?

Upper H 0H0

Upper H Subscript aHa

Your answer is correct.​(b) Determine the critical​ value,

font size increased by 1 font size increased by 1 font size increased by 1 chi Subscript 0 Superscript 2χ20​,

and the rejection region.

Answer 1

Ans:

H₀:The distribution of motivations is 29​% ​rewards,23​%low​ rate,21​% cash​ back,8% ​discounts, and 19​% other.

Ha:The distribution of motivations differs from the claimed or expected distribution.

Ha is claim

df=5-1=4

alpha=0.1

critical chi square value=CHIINV(0.1,4)=7.779

Reject H0,if chi square>7.779

Response	old survey	new survey(fo)	Expected freq(fe)	(fo-fe)^2/fe
Rewards	29%	112	123.25	1.027
Low rates	23%	97	97.75	0.006
cash back	21%	109	89.25	4.370
discounts	8%	47	34	4.971
Other	19%	60	80.75	5.332
Total	100%	425	425	15.706

Test statistic:

Chi square=15.706

df=5-1=4

p-value=CHIDIST(15.706,4)=0.0034

Reject the null hypothesis.

There is sufficient evidence to support the claim.