A statistical test is performed for assessing if men have a longer mean nose length than women. The p-value is 0.225. Which of the following is the most appropriate way to state the conclusion?? a. Men have a longer mean nose length than women.
b. The probability is 0.225 that men and women have the same mean nose length.
c. The mean nose lengths of the populations of men and women are identical.
d. There is not enough evidence to say that men have a longer mean nose length than women.

The most appropriate way to state the conclusion is:

d. There is not enough evidence to say that men have a longer mean nose length than women.

Step-by-step explanation:

We have the result of a hypothesis test.

The claim was that men have a longer mean nose length than women.

That means that the alternative hypothesis states that men's mean nose length is higher than the women's mean nose length.

The P-value of the test is 0.225, which for any usual significance level is large enough to fail to reject the null hypothesis. Then, there is no enough evidence to support the claim that men have a longer mean nose length than women.

a. Men have a longer mean nose length than women.

FALSE. There is no enough evidence to support the claim.

b. The probability is 0.225 that men and women have the same mean nose length.

FALSE. That is not the meaning of the P-value.

c. The mean nose lengths of the populations of men and women are identical.

FALSE. We can not claim that the null hypothesis is true, even when we havo no enough evidence to reject it.

d. There is not enough evidence to say that men have a longer mean nose length than women.

TRUE. This is the the most appropriate way to state the conclusion.

answer for #1 is c

answer for #2 is d

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b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: