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 230.2 sec and a standard deviation of 53.67 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?

​One-Sample T

Test of

muequals=210

vs

greater than>210

​95% Lower

N

Mean

StDev

SE Mean

Bound

T

P

4040

230.20230.20

53.6753.67

8.498.49

215.90215.90

2.382.38

0.0110.011

Answer 1

Sol:

Ho:mu=210

Ha:mu>210

alpha=0.05

t=xbar-mu/s/sqrt(n)

=(230.2-210)/(53.67/sqrt(40))

t= 2.380399

t=2.38

df=n-1=40-1=39

p value right tail

==T.DIST.RT( 2.380399,39)

=0.011138461

p=0.011

p<alpha

0.011<0.05

Reject Ho

Accept Ha

Conclusion:

There is suffcient statistical evidence at 5% level of significance to conlcude that the sample is from a population of songs with a mean greater than 210 sec.