Answer:
Step-by-step explanation:
Look at the picture.
The formula of an area of a triangle:
<em>b</em><em> - base</em>
<em>h</em><em> - height</em>
<em />
We need a length of a height.
Use the Pythagorean theorem:
We have:
Substitute:
<em>subtract 25 from both sides</em>
Calculate the area:
Answer:
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 height of men actually its significant lower than 26 so then the specification is satisfied.
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 at least 26 mpg, 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:
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:
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 height of men actually its significant lower than 26 so then the specification is satisfied.
Part A
Purchase Value of Anna's Car in 2015 = $36,000
Depreciated Value of Anna's Car in 2017 = $25,000
We know that the value of the car is depreciating linearly.
From the above data, we can see that the value of the car has reduced by $36,000-$25,000 = $11,000 over 2 years.
⇒ Per year the value has been depreciated by
⇒ Per year the value has been depreciated by $5,500
So if the value of a car in 2015 is V₀ then value of the car after t years can be determined by the below function:
V (t) = V₀ - (t*5,500), where t indicates the years passed since 2015
OR V (t) = 36,000 - (t*5,500), where t indicates the years passed since 2015
Part B
Suggested value of Anna's car for trade in option in 2018 = $15,000
In 2018, 3 years would have been passed since 2015. Using the value of t = 3 in the function determined in Part A:
V(3) = V₀ - (3*5,500)
⇒ V(3) = 36,000 - (16,500)
⇒ V(3) = $19,000
From the above calculations, we can see that the value of the car in 2018 should be $19,000, however the suggested value for trade in is indicated as $15,000 which is lower than what the value of the car should be. Hence, basis linear depreciation, the $15,000 value is not fair for the car in 2018.