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Alina [70]
3 years ago
10

An automobile manufacturer has given its van a 31.3 miles/gallon (MPG) rating. An independent testing firm has been contracted t

o test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 140 vans, they found a mean MPG of 31.1. Assume the population standard deviation is known to be 1.3. A level of significance of 0.02 will be used. State the null and alternative hypotheses.
Mathematics
1 answer:
Fynjy0 [20]3 years ago
4 0

Answer:

z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82  

The p value for this case would be given by:

p_v =2*P(z  

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 31.3 MPG

Step-by-step explanation:

Information given

\bar X=31.1 represent the sample mean  

\sigma=1.3 represent the population standard deviation

n=140 sample size  

\mu_o =31.3 represent the value that we want to test  

\alpha=0.02 represent the significance level for the hypothesis test.  

z would represent the statistic

p_v represent the p value

Hypothesis to test

We want to test if the true mean is equal to 31.3 MPG, the system of hypothesis would be:  

Null hypothesis:\mu =31.3  

Alternative hypothesis:\mu \neq 31.3  

Since we know the population deviation, the statistic is given by

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

Replacing we got:

z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82  

The p value for this case would be given by:

p_v =2*P(z  

For this case since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 31.3 MPG

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natita [175]

Answer:

In the first account was invested \$3,000  at 3%

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Step-by-step explanation:

we know that

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where

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in this problem we have

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substitute in the formula above

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Second account

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substitute in the formula above

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I=350-0.05x

Remember that

The interest is equal to \$290

so

Adds the interest of both accounts

0.03x+350-0.05x=\$290

0.05x-0.03x=350-290

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therefore

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3 years ago
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To solve this, we are going to use the surface are of a sphere formula: A=4 \pi r^2
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We know for our problem that A=2122.64 and \pi =3.14, so lets replace those vales in our formula:
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2122.64=4(3.14)r^2
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r^2=\frac{2122.64}{12.56}
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r=+or- \sqrt{169}
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Since the radius of a sphere cannot be a negative number, r=13.

We can conclude that the radius of a sphere with surface area <span>2,122.64 </span>in^2 is 13 in.
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Brrunno [24]

Answer:

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