The perimeter of a rectangle is given by the formula,
We substitute,
and
into the above formula to obtain the expression,
We now group the x and y terms on the Left Hand Side of the equation to get.
We now divide through by 2 to get,
Therefore the width of the rectangle is
Answer:
The degrees of freedom first given by:
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960
Step-by-step explanation:
Information given
5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.
System of hypothesis
We want to test if the true mean is higher than 5, the system of hypothesis are :
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
The degrees of freedom first given by:
Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:
And for this case the rejection region would be:
b) Reject H0 if tcalc >1.7960