Assume that a simple random sample has been selected from a nomally distributed

Question

Assume that a simple random sample has been selected from a nomally distributed population and test the given claim. Identily the nul and aternaive hypotheses, test statistic, Pvalue, and state the final condlusion 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 220.5 sec and a standard deviason of 55.79 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 resuts suggest about the advice given in the manual? Click the icon to view the Minitab display What are the hypotheses? on H0: > 210 sec O c. Mritab display H, : s 210 sec Ho: . 210 sec H1 : $210 sec One-Sample T Test of mu 210 vs >210 95% Lower dentify the best statistic t (Round to two decimal places as needed.) Identify the P value. The P-value is (Round to tree deomal places as needed.) State the final conclusion that addresses the original claim Choose the oomect answer below O A. 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 B. 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. OC. Reject Ho. There is sufficient evidence to support the claim that the sample is from a popuiation of songs with a mean length greater than 210 sec. OD. Reject Ho- There is insufficient evidence to support the clalim that the sample is from a population of songs with a mean length greater than 210 sec Bound 20664 1.19 0.121 N Mean StDev SE Mean 40 220.50 55.79 8.82 Print Done Click to select your answeris) 0 A. The results suggest that 220.5 seconds is the best song length. O B. The results are inconclusive because the ° C. The results do not suggest that the advice of writing a 0 D. The average length of a hit song is constantly changing song that must be no longer than 210 seconds is not sound advice. h results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. Click to select your answerls). Save for Later 3 4 5 6

Explanation / Answer

Given that,
population mean(u)=210
sample mean, x =220.5
standard deviation, s =55.79
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 =220.5-210/(55.79/sqrt(40))
to =1.1903
| to | =1.1903
critical value
the value of |t | with n-1 = 39 d.f is 1.685
we got |to| =1.1903 & | t | =1.685
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value :right tail - Ha : ( p > 1.1903 ) = 0.12056
hence value of p0.05 < 0.12056,here we do not reject Ho
ANSWERS
---------------
null, Ho: =210 , alternate, H1: >210
test statistic: 1.19
p-value: 0.121
decision: Option B. failed to reject Ho, there is insuffcient evidence to support the claim
Option D: it suggest that the adice of writing a song must be no longer than 210 second

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