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erastova [34]
3 years ago
9

PLEASEE HELP MATHHH

Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
3 0
F(x) = -2x^2 - 3x + 5 for x = - 3
f(-3) = -2(-3)^2 -3(-3) + 5
f(-3) = -18 + 9 + 5
f(-3) = -4
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Congress regulates corporate fuel economy and sets an annual gas mileage for cars. A company with a large fleet of cars hopes to
attashe74 [19]

Answer:

a) Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

b) X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c) t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

p_v =P(t_{(49)}>2.81)=0.0035  

d) If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation  

\bar X=32.12 represent the sample mean  

s=4.83 represent the sample standard deviation

n=50 sample size  

\mu_o =30.2 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:  

Null hypothesis:\mu \leq 30.2  

Alternative hypothesis:\mu > 30.2  

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:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}  (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".  

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

X \sim N(\mu=32.12, \sigma=4.83)

And the distribution for the random sample is given by:

\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)

c. Perform the test and calculate P-value

Calculate the statistic

We can replace in formula (1) the info given like this:  

t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=50-1=49  

Since is a one right tailed test the p value would be:  

p_v =P(t_{(49)}>2.81)=0.0035  

d. State your conclusion.

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.  

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

6 0
3 years ago
Lxl=10 what is the answer
Svetradugi [14.3K]

Answer:

10

Step-by-step explanation:

The absolute value of 10 is 10. Algebraically speaking, the absolute value of a number x takes x and makes it positive.

6 0
2 years ago
T had 53,790 miles onit. They had the car for 8.25 years. On average, how many miles did they drive per year?
liq [111]

Answer: ‭6,520‬ miles per year

Step-by-step explanation:

They had driven the car for 53,790 miles in 8.25 years.

The average number of number of miles driven per year is:

= 53,790 / 8.25 years

= ‭6,520‬ miles per year

<em>They drove an average of ‭6,520‬ miles per year.</em>

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2 years ago
Solve the equation:<br><br> (x^4 - x + y)dx - xdy=0
algol [13]
Keeping in mind that "dx" is the delta x, or differential over the x-axis, whilst "dy" is the delta y or differential over the y-axis,

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5 0
3 years ago
The area of a rectangular window is 6525cm2. If the length of the window is 87cm, what is its width?
nataly862011 [7]

Answer:

width= 75 cm

Step-by-step explanation:

We need to recall the formula to calculate the area of a rectangle, since we are dealing with a rectangular window:

Area of rectangle = width * length

therefore, since they give us the window's area: 6525 cm^2, and also the window's length: 87 cm, we just need to replace those values in the area formula and solve for the unknown "width". We do such by dividing both sides of the equation by 87 cm in order to isolate the unknown on one side of the equal sign;

6525cm^2 =87cm*width\\\frac{6525cm^2}{87cm} =width\\width=75cm

6 0
3 years ago
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