In: Statistics and Probability
A survey was conducted two years ago asking college
students their top motivations for using a credit card. To
determine whether this distribution haschanged, 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,
4747discounts,
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.
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.