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-valuc. and stale 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 currei hit songs results in a mean length of 241.5 sec and a standard deviation of 56.91 sec. Use a 0.05 significance level and the accompanying Minital 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? Click the icon to view the Minitab display. H_0; mu = 210 sec H_1; mu > 210 sec H_0; mu 210 sec H_0; mu > 210 sec H_1; mu lessthanorequalto 210 sec H_0; mu = 210 sec H_1; mu lessthanorequalto 210 sec Identify the test statistic. t = square box Identify the P-value The P-value is square box.

Explanation / Answer

Part 1

Correct alternative for null and alternative hypothesis is A.

Answer = A

Part 2

Test statistic = t = 3.50 (rounded to two decimal places)

Part 3

P-value = 0.001 (rounded to three decimal places)

[The detail test for more reference is given as below:]

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

210

Level of Significance

0.05

Sample Size

40

Sample Mean

241.5

Sample Standard Deviation

56.91

Intermediate Calculations

Standard Error of the Mean

8.9983

Degrees of Freedom

39

t Test Statistic

3.5007

Upper-Tail Test

Upper Critical Value

1.6849

p-Value

0.0006

Reject the null hypothesis

t Test for Hypothesis of the Mean

Data

Null Hypothesis                m=

210

Level of Significance

0.05

Sample Size

40

Sample Mean

241.5

Sample Standard Deviation

56.91

Intermediate Calculations

Standard Error of the Mean

8.9983

Degrees of Freedom

39

t Test Statistic

3.5007

Upper-Tail Test

Upper Critical Value

1.6849

p-Value

0.0006

Reject the null hypothesis

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