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Assume that a simple random sample has been selected from a normally distribute population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim.
In a manual on how to have a number one song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 242.2 sec and a standard deviation of 53.81 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the manual?
Minitab display
One-Sample T
Test of mu = 210 vs> 210
N 40 Mean 242.20 StDev 53.81 SE Mean 8.51 95% Lower Bound 227.86 T 3.78 P 0.000
What are the hypotheses?
Mean Absolute Deviation To avoid the problem of positive and negative deviations canceling out each other, we can use the Mean Absolute Deviation which is given by
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