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 222.0

sec and a standard deviation of 57.4 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?

Explanation / Answer

Minitab Output:

One-Sample T

Test of mu = 210 vs > 210

95%

                                Lower

N     Mean   StDev SE Mean    Bound     T      P

40 222.000 57.400    9.076 206.709 1.32 0.097

Null and Alternative Hypothesis:

Null Hypothesis:

H0: µ = 210

Alternative Hypothesis:

H1: µ > 210

Test Statistics:

z = 1.32

p-value = .097

p-value is greater than .05 (level of significance); we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that the population mean song time is greater than 210.

The above test results support the statement given in the manual that a song must be no longer than 210 seconds.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.