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Naddika [18.5K]
3 years ago
12

An automobile manufacturer has given its car a 46.7 miles/gallon (MPG) rating. An independent testing firm has been contracted t

o test the actual MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 150 cars, they found a mean MPG of 46.5. Assume the population standard deviation is known to be 1.1. A level of significance of 0.05 will be used. Find the value of the test statistic. Round your answer to two decimal places.
Mathematics
1 answer:
erastova [34]3 years ago
7 0

Answer:

z=\frac{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23    

The p value would be given by:

p_v =2*P(z  

For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG

Step-by-step explanation:

Information given

\bar X=46.5 represent the mean

\sigma=1.1 represent the population standard deviation

n=150 sample size  

\mu_o =46.7 represent the value to verify

\alpha=0.05 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 for this case is 46.7, the system of hypothesis would be:  

Null hypothesis:\mu = 46.7  

Alternative hypothesis:\mu \neq 46.7  

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{46.5-46.7}{\frac{1.1}{\sqrt{150}}}=-2.23    

The p value would be given by:

p_v =2*P(z  

For this case since th p value is lower than the significance level of0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean for this case is significantly different from 46.7 MPG

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You have to write the equation for a line that crosses the point (-4, -7) and is perpendicular to the line

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When you have to determine a line that is perpendicular to a known line, you have to keep in mind that the slope of the perpendicular line will be the negative inverse of the first one.

If for exampla you have two lines, the first one being:

y_1=mx+b

And the second one, that is perpedicular to the one above:

y_2=nx+c

The slope of the second one is the negative inverse of the first one:

n=-\frac{1}{m}

The slope of the given line y=-7/4+4 is m=-7/4

So the slope of the perpendicular line has to ve the inverse negative of -7/4

\begin{gathered} n=-(-\frac{4}{7}) \\ n=\frac{4}{7} \end{gathered}

Considering it has to pass through the point (-4,-7) and that we already determined its slope, you can unse the point slope formula to determine the equation of the perpendicular line:

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replace with the coordinates of the point and the slope and calculate:

\begin{gathered} y-(-7)=\frac{4}{7}(x-(-4)) \\ y+7=\frac{4}{7}(x+4) \\ y+7=\frac{4}{7}x+\frac{16}{7} \end{gathered}

Subtract 7 to both sides of the equation to write it in slope-intercept form:

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Now you can graph both lines

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Step-by-step explanation:

We use the Venn diagram to calculate the desired probabilities.

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