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 232.2 sec and a standard deviation of 54.53 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? LOADING... Click the icon to view the Minitab display. What are the? hypotheses? A. Upper H 0?: muequals210 sec Upper H 1?: mugreater than210 sec B. Upper H 0?: muequals210 sec Upper H 1?: muless than or equals210 sec C. Upper H 0?: muless than210 sec Upper H 1?: mugreater than210 sec D. Upper H 0?: mugreater than210 sec Upper H 1?: muless than or equals210 sec Identify the test statistic. tequals nothing ?(Round to two decimal places as? needed.) Identify the? P-value. The? P-value is nothing. ?(Round to three decimal places as? needed.) State the final conclusion that addresses the original claim. Choose the correct answer below. A. Fail to reject Upper 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 Upper 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. Fail to reject Upper 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. D. Reject Upper 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. What do the results suggest about the advice given in the? manual? A. The results suggest that 232.2 seconds is the best song length. B. The results do not 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 the advice of writing a song that must be no longer than 210 seconds is not sound advice. D. The results are inconclusive because the average length of a hit song is constantly changing. Click to select your answer(s).

Answer 1

One-Sample T

Test of ? = 210 vs > 210

N    Mean StDev SE Mean 95% Lower Bound     T      P
40 232.20    54.53     8.62           217.67    2.57 0.007

TS = 2.57

p-value = 0.007

p-value < 0.05

we reject the null hypothesis

D. Reject Upper 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.