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. Identfy the nul and altemative hypotheses, test statistic, P-value, and state the final conclusion that addresses the oniginal 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 238.9 sec and a standard deviation of 56.94 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? Click the icon to view the Minitab display. What are the hypotheses? 0 B. OA. Ho: > 210 sec H1: s 210 sec ° C. Ho: #210 sec H,: Hs210 sec Ho: = 210 sec H: H> 210 sec Ho: 210 sec D. Idantify the test statistic. Round to two decimal places as needed.) Idantify the P-value. The P-value is(Round to three decimal places as needed.) State the final conclusion that addresses the original daim. Choose the correct answer below. A. Reject Ho-There is sufficient evidence to support the c aim that the sample is from a population of songs with a mean length greater than 210 sec. O B. 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. ° C. Fail to reject H0. There is insufficient evidence to support the dam that the sample is from a population of songs with a ean length greater than 210 sec. O 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. What do the results suggest about the advice given in the manual? A. O B. ° C. 0 D. The results suggest that 2388 seconds is the best song length. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. The results are inconclusive because the verage length of a hit song is constantly changing.

Explanation / Answer

One sample t test

t = (x - 210)/(s/sqrt(n) = (238.9 - 210)/(56.94/sqrt(40)) = 3.21

df = 40 - 1 = 39

one sided, p-value = 0.001

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