Question

Dr. Chung, a renowned nutritionist, has consistently proclaimed the benefits of a balanced breakfast. To substantiate her claim, she asks her participants to go without breakfast for one week. The following week he asks the same participants to make sure they eat a complete breakfast. Following each week, Dr. Chung asks the supervisors of each participant to rate their productivity for that week.

Participant          Performance with Breakfast                       Performance Without Breakfast

#1                                 8                                                                  6
#2                                 6                                                                  6
#3                                8                                                                  5
#4                                  8                                                                  5


Using α = .05, do a one-tailed test of the doctor's hypothesis.

What is your T=

Answer 1

Participent	Performance with breakfast (X)	Performance without breakfast (Y)	d=Y-X	d2
#1	8	6	-2	4
#2	6	6	0	0
#3	8	5	-3	9
#4	8	5	-3	9
		sum	-8	22

The mean difference

Standard deviation of the differences is

T statistics is given by

Under the null hypothesis, this statistic follows a t-distribution with n − 1 degrees of freedom.

Using t distribution table,

The p-value is .0331

Decision rule :

The result is significant at p < .05.

Since the p-value (0.0331) is less than 0.05, there is enough evidence to reject the null hypothesis.

In other words, performance with Breakfast does matter.