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 a = 0.10. Complete parts (a) through (d). Response Old Survey % Rewards 27% Low rates 24% Cash back 22% Discounts 7% Other 20% New Survey Frequency, f 111 96 107 47 64 (c) Calculate the test statistic. X? (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Then interpret the decision in the context of the original claim. Ho. At the 10% significance level, there expected distribution. enough evidence to conclude that the distribution of motivations the claimed or Vi More

critical value is 7.779 I think

Answer 1

Computational Table:

Response	Old Survey %	Frequency (Oi)	Expected Frequency (Ei)	Oi - Ei	(Oi-Ei)2	(Oi-Ei)2/Ei
Rewards	27%	111	27% of 425 = 114.25	-3.75	14.06	0.12
Low rates	24%	96	24% of 425 = 102	-6	36.00	0.35
Cash back	22%	107	22% of 425 = 93.5	13.5	182.25	1.95
Discounts	7%	47	7% of 425 = 29.75	17.25	297.56	10.00
Other	20%	64	20% of 425 = 85	-21	441.00	5.19
Total	100%	425	425			17.615

Test statistic:

$\chi ^{2} = \frac{\sum (Oi-Ei)^{2}}{Ei} = 17.615$

Degrees of Freedom: k-1 = 5-1 = 4

Where, K = Number of Responses = 5

Critical value: For $\alpha$ = 0.10

$\chi _{\alpha ,df}^{2} = \chi _{0.10 ,4}^{2} = 7.779$ ..........Using Chi square table

Conclusion:

Test statistic > critical value, i.e 17.615 > 7.779, That is Reject Ho at 10% level of significance.

Reject Ho. At the 10% level of significance level, there is enough evidence to conclude that the distribution of motivations differs from the claimed or expected distribution.