Question

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null ad 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 227.2 sec and a standard deviation of 54.06 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? 1 Click the icon to view the Minitab display O B. Ho H 210 sec H1:μ>210 sec D. Ho : μ210 sec O A. Ho: H 210 sec H1 : μ 210 sec O C. Ho: H> 210 sec H1: μ 210 sec Identify the test statistic. Round to two decimal places as needed) Identify the P-value The P-value isound to three decimal places as needed.) State the final conclusion that addresses the original claim. Choose the correct answer below O A. 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. O B. 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. OC. 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. O D Reject Ho There is sufficient evidence to support the clai m 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? O A. The results suggest that 227.2 seconds is the best song length. O B. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice ° C. The results are inconclusive because the average length of a hit song is constantly changing

Answer 1

This is a left tailed test.

The null and alternative hypothesis is,

C)

Ho: $\mu$ > 210

Ha: $\mu$ $\leq$ 210

The test statistics,

t = ( $\bar x$ - $\mu$ )/ (s/)

Vn 7l

= ( 227.2 - 210 ) / ( 54.06 /$\sqrt{}$40)

= 2.01

p-value = 0.974

Therefore, p-value > 0.05 , fails to reject Ho

A)

Fails to reject Ho. there is insufficient evidence to support the claim that the sample is from a population of songs with a mean length is greater than 210 sec.

C)

The result are inconclusive becuase the average lentgh of hit song is constantly changing.