Question

Recall again that Rind & Bordia (1996) investigated whether or not drawing a happy face
on customers’ checks increased the amount of tips received by a waitress at an upscale
restaurant on a university campus. During the lunch hour a waitress drew a happy,
smiling face on the checks of a random half of her customers. The remaining half of the
customers received a check with no drawing (18 points).
The tip percentages for the control group (no happy face) are as follows:
45% 39% 36% 34% 34% 33% 31% 31% 30% 30% 28%
28% 28% 27% 27% 25% 23% 22% 21% 21% 20% 18%
8%
The tip percentages for the experimental group (happy face) are as follows:
72% 65% 47% 44% 41% 40% 34% 33% 33% 30% 29%
28% 27% 27% 25% 24% 24% 23% 22% 21% 21% 17%

d. Write null and alternate hypotheses that correspond with your answer to
question #c. If you decided to perform a one-tailed test, make sure and
specify which of the two groups you predict will be higher/lower.

Answer 1

Let denote the average tips received by the waitress for the control and experimental group respectively.

To test: Vs

We would expect the experimental group to tip more.

Given:

To test the pre-requisite of equality of variance to test the equality of means,  

To test: Vs

  

Comparing the test statistic with the critical value F for (23-1,22-1) = (22,21) df

Since, 0.803<2.073, we fail to reject H₀ at 5% level of significance.We may conclude that the variances are equal.

Assuming the data is normal,

The test statistic to test the equality of means is given by:

Substituting the values,

= - 0.54

The critical region of the test is given by t < t_crit

Comparing the test statistic with the critical value t for (23+22-2) df = 43 df at 5% level of significance:

Since, t = -0.54 > -1.682, we fail to reject H₀ at 5% level.We may conclude that no significant difference exist between the tips received from the control and experiment group at 5% level of significance.