Assume that a simple random sample has been selected from a normally distributed
ID: 2949763 • 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 241.2 sec and a standard deviation of 55.34 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?
One-Sample T
Test of mu=210 vs >210
N 40
Mean 241.20
StDev 55.34
SE Mean 8.75
95% lower Bound 226.45
T 3.57
P 0.000
A) Identify the test statistic.
t = ____
?(Round to two decimal places as? needed.)
B) Identify the? P-value.
The? P-value is ____
?(Round to three decimal places as? needed.)
C) State the final conclusion that addresses the original claim. Choose the correct answer below.
A. Reject Ho. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec.
B. Reject Ho. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than210 sec.
C. Fail to reject Ho. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec.
D. Fail to reject Ho there is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210
sec.
D) What do the results suggest about the advice given in the? manual?
A. The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice
B.The results suggest that 241.2 seconds is the best song length
C. The results are inconclusive because the average length of a hit song is constantly changing.
D. The results suggestthat the advice of writing a song that must be no longer than 210 seconds is not sound advice.
Explanation / Answer
A) Here the test statistic is t = 3.57.
B) P-value is 0.000.
C) The final conclusion is, B. Reject Ho. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec.
D) The results suggest, D. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.
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