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3 years ago

If this analysis is based on 15 data pairs, what is the 95% confidence interval for the slope of the regression line?

Mathematics

1 answer:

NemiM [27]3 years ago

8 0

Answer:

A. (-2.28, 3.38)

Step-by-step explanation:

The confidence interval of the slope :

b ± Tcritical*SE

Tcritical at 95%, df = n - 2 = (15 - 2) = 13

Tcritical = 2.160369

b = slope Coefficient = 0.54924

S.E = 1.311

Hence, we have :

Confidence interval = 0.54924 ± (2.160369 * 1.311)

Confidence interval = 0.54924 ± 2.832243759

Lower boundary = 0.54924 - 2.83224 = - 2.283

Upper boundary = 0.54924 + 2.83224 = 3.3814

The answer option is A. (-2.28, 3.38)

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Answer:

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First, let's rewrite both of these dimensions in the same units.

Knowing that:

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Then the dimensions of the space can be rewritten from:

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to:

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So, if we enlarge our original picture by a scale factor K, the new dimensions of the picture will be:

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Now we just need to find a value of K such that:

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While if we solve the equation:

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we get:

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So we got two possible scale factors.

Which one we should take?

Notice that if we wanted to use the larger one (K = 6.5) for the 32cm side. the new length would be:

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This is larger than the 200cm of space that we have

Then we can not select the larger option, we can only take the other value:

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