Answer:
a) One-tailed t-test
b)
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
Step-by-step explanation:
Hello!
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!
