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 241.5 sec and a standard deviation of 56.53 sec. Use a .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

Null Hypothesis:

Ho: Mu = 210

Ie Length of number one song is 210 sec

Alternate Hypothesis:

Ha: Mu > 210

Given,

Xbar (mean length of songs) = 241.5

Std Dev (standard deviation) = 56.53

N(No of songs) = 40

Degrees of freedom = 40-1 = 39

Test Statistics:

T = (xbar – Mu)/ (Std Dev/ n1/2)

T = (241.5 – 210)/ (56.53/sqrt(40)) = 3.52

P-Value:

p-value = tdist(3.52,39,1) = 0.000551

Conclusion:

Since the p-value is less than 0.05, we reject the null hypothesis in favour of alternate hypothesis ie mean length of the songs is greater than 210 seconds.

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