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 227.6 sec and a standard deviation of 54.18 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? A Click the icon to view the Minitab display. What are the hypotheses? O A. Ho:<210 sec H >210 sec O C. Ho: u = 210 sec Hu>210 sec OB. Ho: u = 210 sec Hus 210 sec O D. Ho: u> 210 sec H:us 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. O 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. O 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. O C. 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. O D. 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. What do the results suggest about the advice given in the manual?

Answer 1

Solution :

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 210

H_a : $\mu$ > 210

Test statistic =

= ($\bar x$ - $\mu$) / s / $\sqrt$n

= (227.6 - 210) /(54.18 / $\sqrt$40)

Test statistic = 2.05

P(z > 2.05) = 1 - P(z < 2.05)

                  = 1 - 0.9798

P-value = 0.0202‬

$\alpha$ = 0.05

P-value < $\alpha$

Conclusion

B) Reject H₀ There is sufficient evidence to support the claim that the sample is from a population songs with a mean length greater than 210sec

Suggestion

B) The result suggest that 227.6 seconds is the best song length.