Question

Assume that two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that male king penguins from Marion Island weigh more than female king penguins from Marion​ Island?A. Chi-square
B.t
C.Normal
D.F

Answer 1

Answer:

Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:

B.t

Step-by-step explanation:

Notation

$\bar X_{1}$ represent the mean for male king penguins

$\bar X_{2}$ represent the mean for the female king penguins

$s_{1}$ represent the sample standard deviation for the sample male

$s_{2}$ represent the sample standard deviation for the sample female

$n_{1}$ sample size for the male penguins

$n_{2}$ sample size for the female penguins

t would represent the statistic

Hypothesis

We need to conduct a hypothesis in order to check if the male king penguins weigh more than female king penguins, the system of hypothesis would be:

Null hypothesis:$\mu_{1}=\mu_{2}$

Alternative hypothesis:$\mu_{1} > \mu_{2}$

Since we assume that we don't know the population deviations we need to use a t test to check the hypothesis, and the best answer is:

B.t