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

210210

seconds. A simple random sample of

4040

current hit songs results in a mean length of

244.3244.3

sec and a standard deviation of

53.1953.19

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

What are the​ hypotheses?

A.

Upper H 0H0​:

muμgreater than>210210

sec

Upper H 1H1​:

muμless than or equals≤210210

sec

B.

Upper H 0H0​:

muμequals=210210

sec

Upper H 1H1​:

muμgreater than>210210

sec

C.

Upper H 0H0​:

muμequals=210210

sec

Upper H 1H1​:

muμless than or equals≤210210

sec

D.

Upper H 0H0​:

muμless than<210210

sec

Upper H 1H1​:

muμgreater than>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.

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.

B.

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.

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

sufficientsufficient

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 suggest that

244.3244.3

seconds is the best song length.

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

do not suggestdo not suggest

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

210210

seconds is not sound advice.

D.

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

Answer 1

for hypothesis:option B is correct

test statistic =4.08

p value =0.000

final conclusion :option D i s correct

What do the results suggest about the advice given in the​ manual? option B