Question

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 242.5 sec and a standard deviation of 56.51 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 >210

​95% Lower

N Mean StDev SE Mean Bound T P

40 242.50 56.51 8.94 227.45 3.64 0.000

Answer 1

To test,

H0:​​​​​​

H1:​​​​​​

We reject null hypothesis when p value is less than level of significance or ​​​​​​

Here, =0.05

p value =0.000

Hence as p value < 0.05 we reject null hypothesis.

We conclude that there is sufficient evidence to support the claim that sample is from a population of songs with a mean greater than 210 sec.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. Thank you