Question

Suppose 6 pairs of hogs are used in an experiment to determine if a dietary supplement can increase weight gain. Each pair of hogs are full siblings. One sibling is randomly assigned to receive the dietary supplement. The other sibling receives a supplement that does not contain the active ingredient believed to affect weight gain. The gains in pounds are provided below:

Sibling Treatment Weight Gain Placebo Weight Gain

1 70.4 69.3
2 38.2 37.2
3 59.7 58.7
4 40.3 39.3
5 93.5 92.5
6 50.7 49.6

Construct a statistical hypothesis test to test the research question "Is there significant evidence that the supplement increases weight gain?"

a. State the null and alternative hypotheses.
b. Compute a test statistic.
c. Find the rejection region or p-value. Either one is fine.
d. Provide a scientific conclusion.

Answer 1

Explanation:

Corresponding weight gains between siblings that received supplement and month and siblings that did not receive supplement.

The data for the test are the differences between the weight gains of siblings that received supplement and siblings that did not receive supplement.

μd = weight gains of siblings that received supplement minus the weight gains of siblings that did not receive supplement.

received not received diff

70.4 69.3 1.1

38.2 37.2 1

59.7 58.7 1

40.3 39.3 1

93.5 92.5 1

50.7 49.6 1.1

Sample mean, xd

= (1.1 + 1 + 1 + 1 + 1 + 1.1)/6 = 1.03

xd = 1.03

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (1.1 - 1.03)^2 + (1 - 1.03)^2 + (1 - 1.03)^2+ (1 - 1.03)^2 + (1 - 1.03)^2 + (1.1 - 1.03)^2 = 0.0134

Standard deviation = √(0.0134/6

sd = 0.047

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 6 - 1 = 5

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (1.03 - 0)/(0.047/√6)

t = 53.68

We would determine the probability value by using the t test calculator.

p < 0.00001

Assume alpha = 0.05

Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, there is no significant evidence that the supplement increases weight gain