Question

A researcher hypothesizes that electrical stimulation of a region of the ventromedial hypothalamus will result in appetite suppression. To test this, one set of rats is given electrical stimulation, while a control group does not. Rats are subsequently given unrestricted access to sugar pellets for 5 minutes, and the number of pellets eaten is recorded.

a. Use the appropriate test of hypothesis to determine whether or not the treatment rats consume fewer pellets. Use α = .05

No Stimulation: 12, 7, 3, 11, 8,5,14,7,9,10 Stimulation: 8,7,4,14,6,7,12,5,5

b. Based on these findings, what is the exact probability of a Type 1 error occurring?

Answer 1

Given data,

[No simulation ]

Data = 12, 7, 3, 11, 8, 5, 14, 7, 9, 10

Mean (mA) = 8.6

SD(n-1) = 3.3065

n = 10

[Simulation]

Data = 8, 7, 4, 14, 6, 7, 12, 5, 5

Mean (mB) = 7.555

SD(n-1) = 3.3582

n = 9

a.

Two-sample t-test,

Hypothesis is,

Ho (Null hypothesis) : μA = μB

Ha (Alternative hypo) : μA > μB

mA = 8.6,

mB = 7.555

df = 17

We know that,

t = 0.6824

The corresponding p value is,

p = 0.2521

--> Ho was not rejected

Since the p value is greater than the level of significance the null hypothesis is rejected.

b.

Type I error occurs when the null hypothesis is true and we reject it.

Therefore, the exact probability of type 1 error occurring is 0.05