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 statics, P-value, and state the final conclusion that addresses the original claim. In a manual on how to have a number one song, t is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results n a mean length of 235 3 sec and a standard deviation of 53 85 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? Click the icon to view the Minitab display What are the hypotheses? A. H_0: mu 210 sec B. H_0: mu = 200 sec H_1: mu > 210 sec C. H_0: mu > 200 sec H_1: mu lessthanorequalto 210 sec D. H_0: mu = 200 sec H_1: mu lessthanorequalto 210 sec Identify the test statistics. _____ (Round to two decimal places as needed.) Identify the P-value. The P value is _____ (Round to three decimal places as needed.) State the final conclusion that addresses the original claim Choose the correct answer below. A. 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. B. Reject H_0. 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. C. Fall to reject H 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. D. Fail to reject H 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. What do the results suggest about the advice given in the manual? A The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not second advice. B. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. C. The results suggest that 235.3seconds is the best song length. D. The results are inconclusive because the average length of a song is continuously changing. 1 Mintab display

Explanation / Answer

a) option B) is correct

b) t =(Xbar - mean )/(s/sqrt(n))

= (235.3-210)/(53.85/sqrt(40))

=2.97142

this follow t-distribution with n-1= 49 degree of freedom

p-value = P(t >2.97142) = 0.0023

since p-value < alpha= 0.05

we reject the null and there is sufficient evidence that mean > 210

option A) is correct

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