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 anual 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
40current hit songs results in a mean length of 235.4 sec and a standard deviation of 56.67sec. Use a0.05 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.

One-Sample T

95% Lower

N

Mean

StDev

SE Mean

Bound

T

P

40

235.40

56.67

8.96

220.30

2.83

0.004

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

1.What is Ho______? H1 _______?
2.Identify the test statistic ____?
3.Indentify the p-value ___?
4.3.State the final conclusion that addresses the original claim. Choose the correct answer below.

a.Fail to reject Ho.There is sufficient evidence to support the claim that the sample is from a population greater than 210 sec
b.Reject Ho. There is sufficient evidence to support the claim that the sample is from a population greater than 210 sec.
c.eject Ho. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210sec
d. Fail to reject Ho. 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.

5.What do the results suggest about the advice given in the manual?
A.The resultssuggestsuggestthat the advice of writing a song that must be no longer than 210seconds is not sound advice.
B.The results suggest that 235.4seconds is the best song length.
C.The results are inconclusive because the average length of a hit song is constantly changing.
D.The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.

PLEASE WRITE EACH ANSWER OUT ... TY

One-Sample T

Test of mu=210vs>210

95% Lower

N

Mean

StDev

SE Mean

Bound

T

P

40

235.40

56.67

8.96

220.30

2.83

0.004

Explanation / Answer

Part 1:

Ho: µ = 210

H1: µ > 210

Part 2:

Test Statistics:

T = 2.83

Part 3:

p-value = 0.004

Part 4:

b. Reject Ho. There is sufficient evidence to support the claim that the sample is from a population greater than 210 sec.

Explanation:

Here the p-value is less than the level of significance (.004<.05); the null hypothesis can be rejected.

Part 5:

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

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