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 α=0.025.

Old Survey %   New Survey Frequency, f
Rewards    29%   110
Low rates   23%   98
Cash back   21%  109
Discounts   8% 47
Other 19% 61

X2/0= 11.143

Calculate the test statistic.

Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim.

Answer 1

The Hypothesis

H0: The top motivations is distributed as is given

Ha: The distribution differs from that as stated

The Test Statistic:

Each expected cell = (% / 100) * 425

	Observed	Expected %	Expected	(O-E)2	(O-E)2/E
Rewards	110	29	123.25	175.6	1.42440
Low Rates	98	23	97.75	0.063	0.00060
Cash Back	109	21	89.25	390.1	4.37040
Discounts	47	8	34	169	5.00000
Others	61	19	80.75	390.1	5.00000
Total	425.00	100.00	425.00		15.795

test = 15.795

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The Rejection Rule is that if test is > critical (11.143), Then reject H0.

Since test is > 11.143, Reject H0.

The Conclusion: There is sufficient evidence at the 97.5% significance level to conclude that there is a change in the claimed distribution.

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