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tatyana61 [14]
2 years ago
14

An automobile manufacturer claims that its jeep has a 53.9 miles/gallon (MPG) rating. An independent testing firm has been contr

acted to test the MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 53.7. Assume the standard deviation is known to be 1.8. A level of significance of 0.02 will be used.
Find the value of the test statistic.
Mathematics
1 answer:
Advocard [28]2 years ago
7 0

Answer:

Value of the test statistic, z_{test}  = - 1.17

Step-by-step explanation:

Null hypothesis, H_{0}: \mu = 53.9

Alternative hypothesis, H_{a} : \mu \neq 53.9

Sample mean, \bar{X} = 53.7

Sample size, n = 110

Standard deviation, \sigma = 1.8

Significance level, \alpha = 0.02

The value of the test statistics is given by the formula:

z_{test}  = \frac{\bar{X} - \mu}{\frac{\sigma}{\sqrt{n} } } \\z_{test}  = \frac{53.7 - 53.9}{\frac{1.8}{\sqrt{110} } } \\z_{test}  = - 1.17

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Answer:

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Step-by-step explanation:

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How do you solve the three forms: Slope Y-intercept form Standard Form Point slope form
Nostrana [21]

Answer:An equation in the slope-intercept form is written as

y=mx+b

Where m is the slope of the line and b is the y-intercept. You can use this equation to write an equation if you know the slope and the y-intercept.

Example

Find the equation of the line

Choose two points that are on the line

Calculate the slope between the two points

m=y2−y1x2−x1=(−1)−33−(−3)=−46=−23

We can find the b-value, the y-intercept, by looking at the graph

picture28

b = 1

We've got a value for m and a value for b. This gives us the linear function

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In many cases the value of b is not as easily read. In those cases, or if you're uncertain whether the line actually crosses the y-axis in this particular point you can calculate b by solving the equation for b and then substituting x and y with one of your two points.

We can use the example above to illustrate this. We've got the two points (-3, 3) and (3, -1). From these two points we calculated the slope

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This gives us the equation

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From this we can solve the equation for b

b=y+23x

And if we put in the values from our first point (-3, 3) we get

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If we put in this value for b in the equation we get

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which is the same equation as we got when we read the y-intercept from the graph.

To summarize how to write a linear equation using the slope-interception form you

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Find the y-intercept. This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b.

Once you've got both m and b you can just put them in the equation at their respective position.

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