Question

A number of restaurants feature a device that allows credit card users to swipe their cards at the table. It allows the user to specify a percentage or a dollar amount to leave as a tip. In an experiment to see how it works, a random sample of credit card users was drawn. Some paid the usual way, and some used the new device. The percent left as a tip was recorded and listed below. Using a = 0.05, what can we infer regarding users of the device?

Usual	Device
12.4	12.0
14.2	15.2
11.7	9.9
11.4	12.2
11.9	14.9
11.4	13.4
10.6	12.1
12.1	13.0
14.2	10.3
15.9	13.2
13.9

	a.	There is statistically significant evidence to conclude that users of the device leave larger tips than customers who pay in the usual manner.
	b.	There is statistically significant evidence to conclude that users of the device leave smaller tips than customers who pay in the usual manner.
	c.	There is statistically significant evidence to conclude that users of the device and customers who pay in the usual manner do not differ in the percentage value of their tips.
	d.	There is insufficient statistical evidence to make any conclusions from this data.

Answer 1

A number of restaurants feature a device that allows credit card users to swipe their cards at the table. It allows the user to specify a percentage or a dollar amount to leave as a tip. In an experiment to see how it works, a random sample of credit card users was drawn. Some paid the usual way, and some used the new device. The percent left as a tip was recorded and listed below. Using a = 0.05, what can we infer regarding users of the device?

a.	There is statistically significant evidence to conclude that users of the device leave larger tips than customers who pay in the usual manner.
b	There is statistically significant evidence to conclude that users of the device leave smaller tips than customers who pay in the usual manner.
Answer: c	There is statistically significant evidence to conclude that users of the device and customers who pay in the usual manner do not differ in the percentage value of their tips.
d	There is insufficient statistical evidence to make any conclusions from this data.

= 0.1100

DF = n₁+n₂-2 =19

Table value of t with 19 DF at 0.05 level = 2.0930

Rejection Region: Reject Ho if t < -2.0930 or t > 2.0930

Calculated t = 0.1100, not in the rejection region

The null hypothesis is not rejected.

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.05
Population 1 Sample
Sample Size	11
Sample Mean	12.7
Sample Standard Deviation	1.6143
Population 2 Sample
Sample Size	10
Sample Mean	12.62
Sample Standard Deviation	1.7178
Intermediate Calculations
Population 1 Sample Degrees of Freedom	10
Population 2 Sample Degrees of Freedom	9
Total Degrees of Freedom	19
Pooled Variance	2.7693
Standard Error	0.7271
Difference in Sample Means	0.0800
t Test Statistic	0.1100
Two-Tail Test
Lower Critical Value	-2.0930
Upper Critical Value	2.0930
p-Value	0.9135
Do not reject the null hypothesis