Assume that a simple random sample has been selected from a normally distributed population and test...

Question

Question

Assume that a simple random sample has been selected from a normally distributed population and test...

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

210210

seconds. A simple random sample of

4040

current hit songs results in a mean length of

242.3242.3

sec and a standard deviation of

54.9554.95

sec. Use a

0.050.05

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

210210

sec. What do these results suggest about the advice given in the manual?

LOADING...

Click the icon to view the Minitab display.

What are the hypotheses?

N	Mean	StDev	SE Mean	Bound	T
Test of muequals=210 vs greater than>210

				95% Lower
4040	242.30242.30	54.9554.95	8.698.69	227.66227.66	3.723.72

A.

Upper H 0H0:

muμless than<210210

sec

Upper H 1H1:

muμgreater than>210210

sec

B.

Upper H 0H0:

muμgreater than>210210

sec

Upper H 1H1:

muμless than or equals≤210210

sec

C.

Upper H 0H0:

muμequals=210210

sec

Upper H 1H1:

muμgreater than>210210

sec

D.

Upper H 0H0:

muμequals=210210

sec

Upper H 1H1:

muμless than or equals≤210210

sec

Identify the test statistic.

tequals=nothing

(Round to two decimal places as needed.)

Identify the P-value.

The P-value is

nothing .

(Round to three decimal places as needed.)

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

A.

RejectReject

Upper H 0H0.

There is

sufficientsufficient

evidence to support the claim that the sample is from a population of songs with a mean length greater than

210210

sec.

B.

Fail to rejectFail to reject

Upper H 0H0.

There is

sufficientsufficient

evidence to support the claim that the sample is from a population of songs with a mean length greater than

210210

sec.

C.

Fail to rejectFail to reject

Upper H 0H0.

There is

insufficientinsufficient

evidence to support the claim that the sample is from a population of songs with a mean length greater than

210210

sec.

D.

RejectReject

Upper H 0H0.

There is

insufficientinsufficient

evidence to support the claim that the sample is from a population of songs with a mean length greater than

210210

sec.

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

A.The results

do not suggestdo not suggest

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

210210

seconds is not sound advice.

B.The results

suggestsuggest

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

210210

seconds is not sound advice.

C.The results suggest that

242.3242.3

seconds is the best song length.

D.

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

math Statistics-And-Probability

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Answer 1

Answer #1

null hypothesis:Ho		μ	=	210
Alternate Hypothesis:Ha:		μ	>	210

test statistic t =3.72

P-value is =0.000

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

.The results suggests that the advice of writing a song that must be no longer than 210 seconds is not sound advice.

Add a comment

Answer 2

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