Answer:


Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old
Step-by-step explanation:
Data given
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean is less than 36 years old, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
And replacing we got:
Now we can calculate the critical value but first we need to find the degreed of freedom:

So we need to find a critical value in the t distribution with df =21 who accumulates 0.025 of the area in the left and we got:

Since the calculated values is lower than the critical value we have enough evidence to reject the null hypothesis at the significance level of 2.5% and we can say that the true mean is lower than 36 years old
Answer:

Step-by-step explanation:
This question is asking you to insert two equations, f(x) and g(x), into the equation g(x) - f(x). This will lead to the equation below.

Now we can solve for the equation.

Answer:
1/5^5
Step-by-step explanation:
Flip the equation into a fraction.
:>
Answer:
263.76
Step-by-step explanation:
Assuming the shaded area is the yellow area all we must do is find the area of the small circle and subtract it from the larger circle.
To do this we can use the area of a circle equation:

first we need to find the radius of the large circle which is simply 4+6= 10
so the area would be:

then we find the area of the small circle is

next we evaluate:

Then replace pi with 3.14:
84 · 3.14 = 263.76
And you have your answer!
Hope this helps!