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 240.2 sec and a standard deviation of 54.27 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 A. Ho: = 210 sec ° C. Ho: > 210 sec O B. Ho : = 210 sec H1:>210 sec D. Ho: 210 sec H1 : 210 sec 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 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 insufficient 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. 0 D. 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. ( D. 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 suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice The results suggest that 240.2 seconds is the best song length. The results are inconclusive because the average length of a hit song is constantly changing

Explanation / Answer

Given that,
population mean(u)=210
sample mean, x =240.2
standard deviation, s =54.27
number (n)=40
null, Ho: =210
alternate, H1: >210
level of significance, = 0.05
from standard normal table,right tailed t /2 =1.685
since our test is right-tailed
reject Ho, if to > 1.685
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =240.2-210/(54.27/sqrt(40))
to =3.5195
| to | =3.5195
critical value
the value of |t | with n-1 = 39 d.f is 1.685
we got |to| =3.5195 & | t | =1.685
make decision
hence value of | to | > | t | and here we reject Ho
p-value :right tail - Ha : ( p > 3.5195 ) = 0.00056
hence value of p0.05 > 0.00056,here we reject Ho
ANSWERS
---------------
null, Ho: =210
alternate, H1: >210
test statistic: 3.5195
critical value: 1.685
decision: reject Ho
p-value: 0.00056

OPTION D: Rejec 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

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