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adelina 88 [10]
2 years ago
5

In developing a new gasoline additive, researchers randomly select 10 cars and drive them both with and without the additive. Th

e sample mean difference in gas mileage (mpg with additive - mpg without additive) is 0.41 mpg with a sample variance of 0.16. Assume the differences are from an approximately normal distribution. We want to test the hypothesis that the fuel additive has mean mpg less than the mean mpg without the additive. Calculate the test statistic.
Mathematics
1 answer:
soldi70 [24.7K]2 years ago
7 0

Answer:

The test statistic is t = 3.24.

Step-by-step explanation:

We want to test the hypothesis that the fuel additive has mean mpg less than the mean mpg without the additive.

This means that the null hypothesis is that the difference is less than 0, while the alternate hypothesis is that the difference is 0 or more.

The test statistic is:

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

0 is tested at the null hypothesis:

This means that \mu = 0

Randomly select 10 cars

This means that n = 10

The sample mean difference in gas mileage (mpg with additive - mpg without additive) is 0.41 mpg with a sample variance of 0.16.

This means that X = 0.41, s = \sqrt{0.16} = 0.4

Calculate the test statistic.

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{0.41 - 0}{\frac{0.4}{\sqrt{10}}}

t = 3.24

The test statistic is t = 3.24.

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user100 [1]
When x=-1: \quad (-1)y=-4\qquad\to\qquad y=4\)

Ok that gives us a little more information.
If we implicitly differentiate with respect to t, from the very start, then we can apply our product rule, ya?

x'y+xy'=0

The right side is zero, derivative of a constant is zero.
Where x' is dx/dt and y' is dy/dt.

From here, plug in all the stuff you know:
y' = -3
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4 0
3 years ago
Oliver has 3 times as many rocks in his collection as Katie. Then Oliver collected 75 more rocks and Katie collected 105 more ro
Evgesh-ka [11]

Answer:

The answer to your question is Katie had 15 rocks and Oliver 45 rocks.

Step-by-step explanation:

Conditions

Katie has x amount of rocks

Oliver has 3x amount of rocks

The final amount of rocks

                                    Oliver = 3x + 75

                                     Katie = x + 105

Now, they have the same amount of rocks, then we can equal both equations

                                   3x + 75 = x + 105

Solve for x

                                     3x - x = 105 - 75

                                           2x = 30

                                             x = 30/2

                                             x = 15

Conclusions

At first Katie had 15 rocks and Oliver had 3(15) = 45 rocks

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