Sam drew sticks and circles to solve this problem. Explain how he added. Then write the total.
1 answer:
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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.
Answer:
The solutions are x = -9 , x = -5
Step-by-step explanation:
* Lets find the vertex of the parabola
- In the quadratic equation y = ax² + bx + c, the vertex of the parabola
is (h , k), where h = -b/2a and k = f(h)
∵ The equation is y = x² + 14x + 45
∴ a = 1 , b = 14 , c = 45
∵ h = -b/2a
∴ h = -14/2(1) = -14/2 = -7
∴ The x-coordinate of the vertex of the parabola is -7
- Lets find k
∵ k = f(h)
∵ h = -7
- Substitute x by -7 in the equation
∴ k = (-7)² + 14(-7) + 45 = 49 - 98 + 45 = -4
∴ The y-coordinate of the vertex point is -4
∴ The vertex of the parabola is (-7 , -4)
- Plot the point on the graph and then find two points before it and
another two points after it
- Let x = -9 , -8 and -6 , -5
∵ x = -9
∴ y = (-9)² + 14(-9) + 45 = 81 - 126 + 45 = 0
- Plot the point (-9 , 0)
∵ x = -8
∴ y = (-8)² + 14(-8) + 45 = 64 - 112 + 45 = -3
- Plot the point (-8 , -3)
∵ x = -6
∴ y = (-6)² + 14(-6) + 45 = 36 - 84 + 45 = -3
- Plot the point (-6 , -3)
∵ x = -5
∴ y = (-5)² + 14(-5) + 45 = 25 - 70 + 45 = 0
- Plot the point (-5 , 0)
* To solve the equation x² + 14x + 45 = 0 means find the value of
x when y = 0
- The solution of the equation x² + 14x + 45 = 0 are the x-coordinates
of the intersection points of the parabola with the x-axis
∵ The parabola intersects the x-axis at points (-9 , 0) and (-5 , 0)
∴ The solutions of the equation are x = -9 and x = -5
* The solutions are x = -9 , x = -5
