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4 years ago

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Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the pre

vious 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased; what is the critical value

1 answer:

artcher [175]4 years ago

6 0

Answer: The proportion of new car buyers that trade in their old car has statistically significantly decreased.

Step-by-step explanation:

Since we have given that

p = 48% = 0.48

n = 115

x = 46

So, $\hat{p}=\dfrac{46}{115}=0.40$

So, hypothesis would be

$H_0:\ p=\hat{p}\\\\H_a:p$

So, test value would be

$z=\dfrac{p-\hat{p}}{\sqrt{\dfrac{p(1-p)}{n}}}\\\z=\dfrac{0.48-0.40}{\sqrt{\dfrac{0.48\times 0.52}{115}}}\\\\z=\dfrac{0.08}{0.0466}\\\\z=1.72$

At 10% level of significance, critical value would be

z= 1.28

Since 1.28 < 1.72

So, we will reject the null hypothesis.

Hence, the proportion of new car buyers that trade in their old car has statistically significantly decreased.

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Svet_ta [14]

<h2>Answer</h2>

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<h2>Explanation</h2>

First, we are going to translate the center of dilation to the origin. Since the center of dilation is (2, -2) we need to move two units to the left (-2) and two units up (2) to get to the origin. Therefore, our first partial rule will be:

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Now, the only thing left to create our actual rule is going back from the origin to the original center of dilation, so we need to move two units to the right (2) and two units down (-2)

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Now that we have our rule, we just need to apply it to each point of our triangle to perform the required dilation:

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$R'=(\frac{5}{3} (2)-\frac{4}{3} ,\frac{5}{3}(1)+ \frac{4}{3})$

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$S'=(\frac{10}{3} -\frac{4}{3} ,-\frac{10}{3}+ \frac{4}{3})$

$S'=(2,-2)$

$T=(-1,-2)$

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$T'=(-\frac{5}{3} -\frac{4}{3} ,-\frac{10}{3}+ \frac{4}{3})$

$T'=(-3,-2)$

Now we can finally draw our triangle:

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