Assume that a simple random sample has been selected from a normally distributed

Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, 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 228.9 sec and a standard deviation of 55.63 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?

Explanation / Answer

Claim: it is stated that a song must be no longer than 210 seconds

H0: Mu=210

H1: Mu>210

alpha:5%

Test statictic:

sample mean=228.9 and standard deviation=55.63 and n=40

t=2.149

Conclusion:

P value=0.019 < 0.05

Since P<0.05, we reject the Ho. Hence claim is significant

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