A man is hiking in Death Valley. He starts at an elevation of 65 feet above sea level and descends to an elevation 30 feet below
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We have two samples, A and B, so we need to construct a 2 Samp T Int using this formula:
In order to use t*, we need to check conditions for using a t-distribution first.
- Random for both samples -- NOT STATED in the problem ∴ <u><em>proceed with caution</em></u>!
- Independence for both samples: 130 < all items sold at Location A; 180 < all items sold at Location B -- we can reasonably assume this is true
- Normality: CLT is not met; <u>n < 30</u> for both locations A and B ∴ <u><em>proceed with caution</em></u>!
<u>Since 2/3 conditions aren't met, we can still proceed with the problem but keep in mind that the results will not be as accurate until more data is collected or more information is given in the problem.</u>
<u>Solve for t*:</u>
<u></u>
We need the <u>tail area </u>first.
Next we need the <u>degree of freedom</u>.
The degree of freedom can be found by subtracting the degree of freedom for A and B.
The general formula is df = n - 1.
- df for A: 13 - 1 = 12
- df for B: 18 - 1 = 17
- df for A - B: |12 - 17| = 5
Use a calculator or a t-table to find the corresponding <u>t-score for df = 5 and tail area = .05</u>.
- t* = -2.015
Now we can use the formula at the very top to construct a confidence interval for two sample means.
Substitute the variables into the formula: .
Simplify this expression.
Adding and subtracting 3.73139 to and from -16 gives us a confidence interval of:
If we want to <u>interpret</u> the confidence interval of (-20.5707, -11.4293), we can say...
<u><em>We are 90% confident that the interval from -20.5707 to -11.4293 holds the true mean of items sold at locations A and B.</em></u>