What is a linear equation represents a line with a slope of −7 and a y-intercept of 12?
2 answers:
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Answer:
The required piece-wise linear function is
Step-by-step explanation:
Consider the provided information.
Let x represents the number of hours and S(x) represents the depth of snow.
There was no snow on the ground when it started falling at midnight at a constant rate of 1.5 inches per.
That means the depth of snow will be:
At 4:00 a.m., it starting falling at a constant rate of 3 inches per hour,
From mid night to 4:00 a.m the depth of snow will be 1.5×4=6 inches.
If we want to calculate the total depth of snow from midnight to 7:00 am we need to add 6 inches in 3(x-4) where 4≤x<7
Therefore,
7:00 a.m. to 9:00 a.m., snow was falling at a constant rate of 2 inches per hour.
From mid night to 7:00 a.m the depth of snow will be 3(7-4)+6=15 inches.
If we want to calculate the total depth of snow from midnight to 9:00 am we need to add 15 inches in 2(x-7) where 7≤x≤9
Therefore, the required piece-wise linear function is
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