Assume that simple random sample has been selected form a normally distributed p
ID: 3240265 • Letter: A
Question
Assume that simple random sample has been selected form 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 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 240.3 sec and a standard deviation of 53.78 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 tan210 sec. What do these results suggest about the advice given in the manual? What are the hypotheses? H_0: mu = 210 sec H_1: mu > 210 sec H_0: mu 210 sec H_1: 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 = (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 State the final conclusion that addresses the original claim. Choose the correct answer below. Fail to 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. 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. Fail to 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. 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. What do the results suggest about the advice given in the manual? he results suggest that 240.3 seconds is the best song length. The results are because the average length of a hit song is changing The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.Explanation / Answer
The statistical software output for this problem is:
One sample T hypothesis test:
: Mean of population
H0 : = 210
HA : > 210
Hypothesis test results:
Hence,
Hypotheses: Option A is correct.
t = 3.56
P - value = 0.001
Final conclusion: Option D is correct.
What result suggests: Option D is correct.
Mean Sample Mean Std. Err. DF T-Stat P-value 240.3 8.5033646 39 3.5632954 0.0005