If σ is not known, then we cannot use the test statistic: Z=√nσx−μ
We will instead use the test-statistic: Z=√nsx−μ
So at the very least we must know the sample standard deviation, s.
Furthermore we will be using a t-distribution instead of our standard normal distribution to find our fail to reject region and our rejection region.
“Redline motorcycles” is a company that fixes and tunes motorcycles. A sample of 75 of their motorcycles had an average of 135hp, and a standard deviation of 35hp. Test the following claims with a 99% confidence level:
Mean hypothesis testing with t-distribution
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