Question

New Survey 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 =0.05. Complete parts (a) through (d). Response Old Survey % Rewards 28% Low rates 24% Cash back 21% Discounts 7% Other 20% Frequency, 110 97 108 47 63 a. State Ho and H, and identify the claim. What is the null hypothesis, H? O A. The distribution of motivations is 28% rewards, 24% low rate, 21% cash back, 7% discounts, and 20% other. OB. The distribution of motivations differs from the expected distribution O C. The distribution of motivations is 110 rewards 97 low rate, 108 cash back, 47discounts, and 63 other. What is the alternate hypothesis, H,? O A. The distribution of motivations is 28% rewards, 24% low rate, 21% cash back, 7% discounts, and 20% other. O B. The distribution of motivations is the same as the claimed or expected distribution O C. The distribution of motivations differs from the claimed or expected distribution Which hypothesis is the claim? оно Ha

Answer 1

a) Correct answer: Option (A) for H0

Correct answer: Option (C) for H1

Claim: Option (B) Ha

b) Critical X^2: 9.488 at 5% los and 4 df

Reject region : Option (A) Chi-square > Chi-square0

c)

From the given data

	Observed		Expected
Response	Freq (Oi)	Probability	Freq. (Ei)	(Oi-Ei)	(Oi - Ei)^2	(Oi-Ei)^2 /Ei
Rewards	110	0.28	119	-9	81	0.6807
Low rates	97	0.24	102	-5	25	0.2451
Cash Back	108	0.21	89.25	18.75	351.5625	3.9391
Discounts	47	0.07	29.75	17.25	297.5625	10.0021
Others	63	0.20	85	-22	484	5.6941
Total:	425	1.00	425		Chi-square=	20.5611

Test Statistic, X^2: 20.561

d) We reject H0. At the 5% significance level, there is enough evidence to conclude that the distribution of motivations are difference or a change the claimed or expected distribution