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

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

represent the mean for male king penguins

represent the mean for the female king penguins

represent the sample standard deviation for the sample male

represent the sample standard deviation for the sample female

sample size for the male penguins

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:

Alternative hypothesis:

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

clock

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: