My teacher asked me to round 71,500 to the nearest thousand. I think that the answer is 72,000. Did I round correctly?
2 answers:
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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.
Given:
Point (7,12) is rotated 1260° counterclockwise about the origin.
To find:
The x-coordinate of the point after this rotation.
Solution:
If a point is rotated 360 degrees then its coordinates remains unchanged.
If a point is rotated 180 counterclockwise about the origin degrees, then
We know that,
After rotation the coordinates of points remains same, i.e., (7,12). So, after that (7,12) is rotated 180° counterclockwise about the origin.
The point (7,12) becomes (-7,-12) after rotation of 1260° counterclockwise about the origin.
Therefore, the x-coordinate of the required point is -7.