Using the slope concept, considering it's value of 0.3415, it is found that the angle of elevation is of 18.86º.
<h3>What is a slope?</h3>The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
Hence, we have that:
More can be learned about the slope concept at brainly.com/question/18090623
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Option B is right perpendicular bisectors of the sides of the triangle
<h3>What circumcircle?</h3>If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle. We have in a triangle there are some properties inherent.
One is the perpendicular bisectors of all sides are concurrent. These three concur at a point called the circumcentre of the triangle.
When we draw a perpendicular bisector for a side AB, we get that all points on the perpendicular bisector are equidistant from A and B.
When we take the point of intersection of the perpendicular bisector of AB and BC, we have the intersecting point S(say) is equidistant from A and B and also from B and C
In short, this is equidistant from all 3 vertices and hence is the centre of the circumcircle of triangle ABC
Therefore Option B is right perpendicular bisectors of the sides of the triangle.
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Answer:
a)Null hypothesis:
Alternative hypothesis:
b)
Since is a two sided test the p value would be:
c) If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 24.57 at 5% of signficance.
d) For this case since we have a two tailed test we need to find two critical values and we need 0.025 of the area on each tail of the t distribution with 29 degrees of freedom. The critical values are given by:
And the rejection zone would be given by:
Since pur calculated value is not on the rejection zone we Fail to reject the null hypothesis.
Step-by-step explanation:
The mean hourly wage for employees in goods-producing industries is currently $24.57. Suppose we take a sample of employees from the manufacturing industry to see if the mean hourly wage differs from the reported mean of $24.57 for the goods-producing industries.
a. State the null and alternative hypotheses we should use to test whether the population mean hourly wage in the manufacturing industry differs from the population mean hourly wage in the goods-producing industries.
We need to conduct a hypothesis in order to check if the mean is equal to 24.57 or not, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
b. Suppose a sample of 30 employees from the manufacturing industry showed a sample mean of $23.89 per hour. Assume a population standard deviation of $2.40 per hour and compute the p-value.
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
If we analyze the size for the sample is = 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:
(1)
t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
c. With α = 0.05 as the level of significance, what is your conclusion?
If we compare the p value and the significance level assumed we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 24.57 at 5% of signficance.
d. Repeat the preceding hypothesis test using the critical value approach.
For this case since we have a two tailed test we need to find two critical values and we need 0.025 of the area on each tail of the t distribution with 29 degrees of freedom. The critical values are given by:
And the rejection zone would be given by:
Since pur calculated value is not on the rejection zone we Fail to reject the null hypothesis.