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.

Answer 1

Answer:

Explanation:

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(X)       Performance Without Breakfast

(Y)

#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=

Performance with breakfast

mean, X = (8+6+8+8)/4 = 7.5

using the formular, $S = \sqrt{\frac{sum(xi-X)^{2} }{N-1} }$

standard deviation, S =√[ [(8-7.5)² + (6-7.5)² + (8-7.5)² + (8-7.5)²]/(4-1)]

S = 1

Number of sample, N = 4

Performance without breakfast

mean, x = (6+5+6+5)/4 = 5.5

Using the formula as above, standard deviation  

$s = \sqrt{\frac{sum(xi-x)^{2} }{n-1} }$

s =√[ [(6-5.5)² + (6-5.5)² + (5-5.5)² + (5-5.5)²]/4-1]

s = 0.58

n = 4

T is given as follows

$T = \frac{X- x}{\sqrt({\frac{S^{2} }{N} }+\frac{s^{2} }{n} )}$

T = [(X - x)/[(S²/N) + (s²/n)]]

T = [(7.5 - 5.5)/[(1²/4) + (0.58²/4)]]

 T = 3.46