Unformatted text preview: om your random sample. This "difference" may be so small it's of no practical
importance. For example, is it of any practical importance to know that the average
length of all fish in Lake Larry is actually 8.495 inches instead of 8.500 inches?
Probably not. Page 1 of 9 1.
A linear rotary bearing is designed so that the distance between the retaining
rings is 0.875 inch. The quality-control manager suspects that the manufacturing
process needs to be recalibrated and that the mean distance between the retaining
rings is different from 0.875 inch. In a random sample of 36 bearings, she finds
the sample mean distance between the retaining rings to be 0.873 inch with a
sample standard deviation of 0.005 inch.
a) Test the quality-control manager’s claim at the α=0.05 significance level.
Null Hypothesis H0:
Alternate Hypothesis H1:
Significance Level α = Population Mean = 0.875
Population Mean "not equal" 0.875 5% The name of the TI-83/84 calculator function you will be using: T-Test Are the conditions met in order to use this statistical method? Show how you
verified this: Yes. We have a random sample and a large sample size of at least 30, so our
Sampling Distribution for he sample mean should be approximately normal, even if our
population that we're sampling from is not normal.
The values that you entered into your TI-83/84 calculator: μ0 : 0.875
: 0.873 Sx: 0.005 n: 36 μ: "not equal" x ← (show which choice you highlighted) From your calculator’s output give the following:
Test Statistic t = -2.4 Interpret what this value is telling you: Our Test Statistic is 2.4 Standard Errors below the hypothesized population mean of
P-Value = 2.18% Interpret what this value is telling you: There is a 2.18% probability of getting a Test Statistic this far away (or farther away)
from the hypothesized population mean of 0.875 IF the Null Hypothesis is true.
Page 2 of 9 Which one is your conclusion (Click in the box next to your choice):
Failed to Reject H0
Reject H0 and Accept...
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- Winter '08
- Statistics, Statistical hypothesis testing, significance level