8. Assume that a simple random sample has been selected from a normally distribu

Question

8. Assume that a simple random sample has been selected from a normally distributed po m. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. In a manual on pulation 210 seconds. A simple random sample of 40 current hit songs results in a secon acco how to have a number one song, it is stated that a song must be no longer than ds and a standard deviation of 57.48 seconds. Use a 0.05 significance level and the mpanying Minitab display to test the claim that the sample is from a population of songs a mean greater than 210 seconds. What do these results suggest about the advice given in mean length of 240.5 c level anad with the manual? One-Sample T Test of mu = 210 vs > 210 95% Lower N Mean StDev SE Mean Bound T 40 240.50 57.48 0 9.09 225.19 3.36 0.001

Explanation / Answer

From the given results the p-value for the test that mean time is more than 210 seconds is 0.001 which is less than 0.05 which is the level of significance. Now as the p-value < level of significance, therefore the test is significant and we have sufficient evidence here to support the statement that the song length is more than 210 seconds.

This suggests that the advice given in the manual is not correct because from the sample analysis of 40 hit songs we have concluded here that the mean time of the hit songs is greater than 210 seconds.

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