Question

Although more than 81% of total restaurant sales are paid by card (either credit or debit), some customers still prefer to pay with either cash or by using personal checks.

	DF	SS	MS	F	P
Groups		299.11			0.0010
Error	203	4258.94	20.98

The tables above shows an incomplete ANOVA Table with a (simulated randomization) p-value that researchers from Ohio State University constructed to determine if, based on a sample of 206 individuals, the mean amount that customers tip differs between the three payment methods.[1]

Use the descriptive statistics below to find the margin of error for a 95% pairwise comparison of customers who pay using cards to those who pay using cash.

Group	N	Mean	SD
Card	167	0.169	0.041
Cash	33	0.145	0.035

Answer 1

1. The F-statistic is 7.13.

Source	SS	df	MS	F	p-value
Groups	299.1100	2	149.5550	7.13	.001
Error	4,258.9400	203	20.9800
Total	4,558.0500	205

2. The p-value is 0.001.

Since the p-value (0.001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the mean amount differ between the three payment methods.

3. No, the standard deviation of one group is more than double the standard deviation of another group

4. Since the assumptions of the test are not met, we cannot perform the test.