Juile planted a rectangular garden that is 20 feet long. She placed 56 feet of fencing around her garden. Draw and label a sketc
h of her garden what is the width of her garden? What is the area?
1 answer:
Answer:
Step-by-step explanation:
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
She placed 56 feet of fencing around her garden. This means that the perimeter of the garden is 56 feet. If the length of the rectangular garden is 20 feet, i means that
2(20 + W) = 56
Dividing through by 2, it becomes
20 + W = 28
W = 28 - 20
W = 8 feet
The formula for determining the area of a rectangle is expressed as
Area = length × width
Therefore,
Area = 8 × 20 = 160 square feet
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Answer:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0
Step-by-step explanation:
Data given and notation
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)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the mean is lower than 20, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
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:
Part a: P-value
The first step is calculate the degrees of freedom, on this case:
Since is a one sided test the p value would be:
Part b: Conclusion
If we compare the p value and the significance level given we see that
so we can conclude that we have enough evidence to fail reject the null hypothesis, and we can conclude that the true mean is not lower than 20 at 1% of signficance.
a. There is insufficient evidence to reject h^0