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To find the area of a sector of a circle use the next formula:
As the given circle has a outside angle 90º (it is not part of the sector of the circle) subtract the 90º from 360º (total angle of a circle) to find the angle of the sector:
Find the area of the sector with angle 270º:
Answer:
Now we can calculate the p value with the following probability:
The p value is a very low value so then we have enough evidence to reject the null hypothesis and we can conclude that people under the age of forty have vocabularies that are different than those of people over sixty years of age.
Step-by-step explanation:
Information given
represent the mean for sample 1 (younger)
represent the mean for sample 2 (older)
represent the sample standard deviation for 1
represent the sample standard deviation for 2
sample size for the group 2
sample size for the group 2
t would represent the statistic
System of hypothesis
We want to test if that people under the age of forty have vocabularies that are different than those of people over sixty years of age, the system of hypothesis are:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And the degrees of freedom are given by
Replacing the info given we got:
Now we can calculate the p value with the following probability:
The p value is a very low value so then we have enough evidence to reject the null hypothesis and we can conclude that people under the age of forty have vocabularies that are different than those of people over sixty years of age.