The double implication "if and only if" is graphically represented by an arrow pointing in both direction, so the correct writing is
You can use this phrase to help you...
•King
•Henry
•Drinks
•Many cups of
•Chocolate
•Milk
Which also stands for the metric units...
•Kilometer
•Hectometer
•Decameters
•Meter
•Centimeter
•Millimeter
And whenever you need to convert from 1 unit to the next, just jump back and forth on the system
Answer:
b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.
See explanation below.
Step-by-step explanation:
Develop the null and alternative hypotheses for this study?
We need to conduct a hypothesis in order to check if the means for the two groups are different (men have longer mean nose length than women), the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Assuming that we know the population deviations for each group, for this case is better apply a z test to compare means, and the statistic is given by:
(1)
z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.
Let's assume that the calculated statistic is
Since is a right tailed test test the p value would be:
And we know that the p value is 0.225. If we select a significance level for example 0.05 or 0.1 we see that
And on this case we have enough evidence to FAIl to reject the null hypothesis that the means are equal. So then the best conclusion would be:
b. There is not enough evidence to say that the populations of men and women have different mean nose lengths.
What is presented here is an example of a two-column proof, where one side lists the steps in the order in which the author worked and the parallel side explaining the reason behind each step. In the first example, it shows that the equation is given because we did not need any sort of thinking to come to the conclusion that 2/3y +15 = 9. The second step is actually Subtraction of Equality because we are subtracting the integer 15 from both sides, therefore both sides are still equal.
In the third step, the reason provided is simplification. We can infer that this means we will need to combine like terms since the step before has like terms (15 and -15, 9 and -15). If we combine these terms we get 2/3y = -6.
The fourth step of action we can probably take from step three, is to multiply both sides by 3 in order to eliminate the denominator. With that we get, 2y = -18 and can be justified by simplification.
The final step calls for simplification, meaning all we have to do is either add, subtract, divide, or multiply both sides by the same number. We are solving for y, so in order to get y alone we must divide both sides by 2. This is to get rid of any coefficient of the y variable. The final step of this proof is y = -9
Hope this helps!