Dr. Nkrumah studies white-footed mice in the Konza Prairie in Kansas. Recently he has noticed that a new species of grass (martin grass) has appeared in one of his study areas. The seeds of this new plant seemed to be used by the mice as a food source and recent captures of mice in the area indicate that the mice in the area are increasing in overall weight. To determine if this new food source is causing the increase in mice weight Dr. Nkrumah has captured 60 mice from his site. He weighs each mouse and then places each into a separate cage. All the mice are kept in the same chamber, with the same light and temperture conditions. Half of the mice are given a diet consisting of entirely of wheat seeds (normal diet), and the other half are feed a diet that consist of 50% wheat seeds and 50% martin grass seeds.The volume of each diet is the same. He feeds the mice these diets for two weeks and then weighs each mouse.
a. What type of statistical test should Dr. Nkrumah use to analyze this data?
O two-tailed t-test
O chi squared
O paired t-test
O one-tailed t-test
O critical value
b. Identify the null and alternate hypotheses being studied with this experiment.

a) To test if the Martin grass seeds increase the weight of mice, the researcher captured 60 mice and separated them in two groups, all individuals were kept in the same type of chamber, with the same light and temperature, the only difference is that each group was fed with a different diet:

Group 1

n₁= 30 mice

Diet₁: wheat seeds (normal diet)

Variable measured: X₁: Net weight gain of a mouse fed with diet 1 for two weeks.

Group 2

n₂= 30 mice

Diet₂: 50% Wheat seeds and 50% Martin grass seeds

Variable measured: X₂: Net weight gain of a mouse fed with diet 2

To compare the effect of both diets is best to compare the means of both groups, so the parameters of interest are μ₁ and μ₂.

If both variables are considered to have a normal distribution and there are no known values of the population variances. Considering that both groups are independent, the propper statistic to use for the analysis is a t-test.

If the objective is to prove whether or not the Martin grass increases the weight gain on mice, then the test should be one-tailed.

b) As said before, the parameters of interest are μ₁ and μ₂ and the test is one-tailed. The claim is that the Martin grass seeds increase the weight gain, if so, the average net weight gain on mice fed with Martin grass should be greater than the average net weight gain of the mice fed only with wheat, then the hypotheses are:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

I hope this helps!