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Montano1993 [528]
3 years ago
5

Look at the 95% confidence interval and say whether the following statement is true or false. ""This interval describes the pric

e of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area."" Be sure to explain your answer.
Mathematics
1 answer:
zheka24 [161]3 years ago
8 0

Answer:

False

Step-by-step explanation:

Confidence intervals provide a range for a population parameter at a given significance level. The parameter can be mean, standard deviation etc.

In this example population is the prices of the rents of all the unfurnished one-bedroom apartments in the Boston area

significance level is 95%. Thus, the chance being the true population parameter in the given interval is 95%.

But, "This interval describes the price of 95% of the rents of all the unfurnished one-bedroom apartments in the Boston area." statement is false because the population parameter is missing. Confidence interval may describe population mean for example but it does not describe the <em>whole</em> population.

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Answer:

The required equations are

(-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +(6- \frac {9}{\sqrt {10}})\hat k\right)=0 and

(-5 \hat i + 7 \hat j + 8 \hat k )+\lambda \left((10-\frac {3}{\sqrt {10}})\hat i -\hat j +(6+ \frac {9}{\sqrt {10}})\hat k\right)=0.

Step-by-step explanation:

The given parametric equation of the line, L, is x=5+t, y=6, z=-2-3t, so, an arbitrary point on the line is R(x,y,z)=R(5+t, 6, -2-3t)

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\vec P + \lambda \vec{(PR)}=0

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The given equation can also be written as

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The standard  equation of the line passes through the point P_0(x_0,y_0,z_0) and having direction\vec v= a_1 \hat i +a_2 \hat j +a_3 \hat k is

\frac {x-x_0}{a_1}=\frac {y-y_0}{a_2}=\frac{z-z_0}{a_3}=t \;\cdots (iii)

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The line is passing through the point P_0 (5,6,-2) having direction \vec v=\hat i -3 \hat k.

Note that the point Q(5,6,-2) is the same as P_0 obtained above.

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|t(\hat i -3 \hat k)|=3

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For t= \frac {3}{\sqrt {10}}

(-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\frac {3}{\sqrt {10}})\hat i -\hat j +\left(6-3\times \frac {3}{\sqrt {10}})\hat k\right)=0

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and for t= -\frac {3}{\sqrt {10}},

(-5 \hat i + 7 \hat j - 8 \hat k )+\lambda \left((10+\left (-\frac {3}{\sqrt {10}}\right))\hat i -\hat j +(6-3\times \left(-\frac {3}{\sqrt {10}}\right)\hat k\right)=0

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