Assume that a simple random sample has been selected from a normally distributed
ID: 3182034 • Letter: A
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.