Beyond Common Core
Problem 41 of 45s12-041
Four test bars of a new alloy have mean strength 53.3 kN, SD 3 kN. Test : vs : at . Critical : df 3, ; df 4, . Result?
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Solution walkthrough2:08
- A test counts how many standard errors sits above . We use because only is known.
- Standard error: kN, the typical gap between a sample mean and .
- The gap is kN. Divide by the standard error: .
- Degrees of freedom: , so the critical value is . Reject only if is beyond it.
- , so is not in the rejection region: fail to reject . No convincing evidence that .
- Traps: dividing by gives ; df 4 gives ; and is never compared with .