Question

Before the Christmas shopping rush began, a department store had noted that the percentage of customers who use a major credit card, the percentage who use the store’s credit card, the percentage who pay by debit card, and the percentage who pay with cash are all the same, 25% for each. During the Christmas season, in a sample of 200 shoppers, 68 used a major credit card, 42 used the store’s credit card, 45 paid with cash, and 45 paid with a debit card. At a 95% confidence level, test to see if the methods of payment have changed during the Christmas shopping rush. please show your work

Answer 1

Hypothesis :

$H_{0}:P_{1}=P_{2}=P_{3}=P_{4}=0.25$

$H_{1}:P_{i}\neq 0.25$ (at least one Pi is not equal to 0.25 )

Test statistics:

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

Oi =Observed frequency

Ei=Expcted frequency

K number of observation

Ei=200*0.25=50

	Oi	Ei	(Oi-Ei)2	(Oi-Ei)2/Ei
1	68	50	324	6.48
2	42	50	64	1.28
3	45	50	25	0.5
4	45	50	25	0.5
Total	200	200		8.76

$\chi ^{2}=8.76$

Df=n-1=4-1=3

P value : Is the value of the lowets level of singnificance at which we could reject the Null hypothesis H0
Using P value approch ,we reject the null hypothesis

p value at 0.05 leve of significane

P value =0.0326<0.05

Conclusion : result is significant at 0.05 level of significant