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 230.0 sec and a standard deviation of 53.84 sec. Use 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? What are the hypotheses? A. H0: <210 sec H1: >210 sec B. H0: =210 sec H1: 210 sec C. H0: =210 sec H1: >210 sec D. H0: >210 sec H1: 210 sec Identify the test statistic. t=__ (Round to two decimal places as needed.) Identify the P-value. The P-value is __. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Choose the correct answer below. A. Fail to reject H0. 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. B. Fail to reject H0. 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. C. Reject H0. 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. Reject H0. 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. What do the results suggest about the advice given in the manual? A. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. B. The results are inconclusive because the average length of a hit song is constantly changing. C. The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. D. The results suggest that 230.0 seconds is the best song length.

Explanation / Answer

The statistical software output for this problem is:

One sample T hypothesis test:
: Mean of population
H0 : = 210
HA : > 210

Hypothesis test results:

Hence,

Hypotheses: H0: =210 sec H1: >210 sec

Option C is correct.

t = 2.35

p - Value = 0.012

Final Conclusion: Reject H0. 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.

Option D is correct.

Suggestion: The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.

Option A is correct.

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