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

244.2

sec and a standard deviation of

56.24

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?

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Part 1

What are the hypotheses?

A.

H0:

=210

sec

H1:

210

sec

B.

H0:

>210

sec

H1:

210

sec

C.

H0:

=210

sec

H1:

>210

sec

D.

H0:

<210

sec

H1:

>210

sec

Part 2

Identify the test statistic.

t=enter your response here

(Round to two decimal places as needed.)

Part 3

Identify the P-value.

The P-value is

enter your response here.

(Round to three decimal places as needed.)

Part 4

State the final conclusion that addresses the original claim. Choose the correct answer below.

A.

Failtoreject

H0.

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.

B.

Reject

H0.

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.

C.

Failtoreject

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

sec.

D.

Reject

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

sec.

Part 5

What do the results suggest about the advice given in the manual?

A.

The results

donotsuggest

that the advice of writing a song that must be no longer than

210

seconds is not sound advice.

B.

The results are inconclusive because the average length of a hit song is constantly changing.

C.

The results

suggest

that the advice of writing a song that must be no longer than

210

seconds is not sound advice.

D.

The results suggest that

244.2

seconds is the best song length.