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Perform a significance test

mathmari

Well-known member
MHB Site Helper
Apr 14, 2013
4,004
I guess so, assuming your previous approach was correct which seems plausible. (Thinking)
Applying thesame methodas before I get that the confidence interval for the case of 30 hours is $[2.130030132, \ 6.498790828]$.

Determine the confidence interval for the average weight in pounds for a child who watches television for $36$ hours a week and for a child who watches television for $30$ hours a week. Which confidence interval is greater and why?
By greater it is meant larger values not bigger width, right?

If yes, the greater confidence interval is the first one, for the case of 36 hours. How do we justify that? (Wondering)
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,684
Applying thesame methodas before I get that the confidence interval for the case of 30 hours is $[2.130030132, \ 6.498790828]$.
Looking at your graph in post #1, that looks about right. (Nod)

By greater it is meant larger values not bigger width, right?

If yes, the greater confidence interval is the first one, for the case of 36 hours. How do we justify that?
I believe they mean a greater range of the confidence interval. The range is the upper bound minus the lower bound.
Either way, that is also the confidence interval of 36 hours.

The wiki article explains that the range of the confidence interval has 2 parts:
  1. The error due to uncertainty in estimated slope ($\hat\beta_1$) and y-intersection ($\hat\beta_0$). This error is the least close to the center, and grows bigger away from the center.
  2. The error due to scattering from unexplained sources, which is assumed to be normally distributed with equal variance everywhere.
They also show a picture with the confidence band that has a hyperbolic shape (unrelated to this problem):
300px-Okuns_law_with_confidence_bands.svg.png
As you can see, the band is narrowest at the mean X-value, and grows wider in both positive and negative directions.

And indeed, 30 hours is closer to the mean X-value of 31.47 than 36 hours. (Thinking)