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 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 240.1 sec and a standard deviation of 56.13 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? What are the hypotheses? A. H_0: mu = 210 sec H_1: mu lessthanorequalto 210 sec B. H_0: mu 210 sec C. H_0: mu > 210 sec H_1: mu lessthanorequalto 210 sec D. H_0: mu = 210 sec H_1: mu > 210 sec Identify the test statistic. t = Identify the P-value. The P-value is. State the final conclusion that addresses the original claim. Choose the correct answer below. A. Reject H_0. There is to support the claim that the sample is from a population of songs with a mean length greater than 210 sec. B. Fail to reject H_0. 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. C. Reject H_0. 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.

Explanation / Answer

H0 : = 210 sec vs H1: > 210 sec

test statisrics = Xbar / [/sqrt(n)]

test statistics = 240.1 /(56.13/sqrt(40))

t = 27.0537

p value = P(ttable > t calc)

p value = 0.0001 < alpha = 0.05

so we 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.

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