Assume that a simple random sample has been selected from a nomally distributed

Question

Assume that a simple random sample has been selected from a nomally distributed population and test the given claim. Identify the null and alternative hypotheses. est 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 cument hit songs results in a mean length of 235.1 sec and a standard deviation of 57.9 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? O A. Ho: u 0 sec O B. Ho: H 210 sec H1: HS210 sec H1: 210 sec O D. Ho: u> 210 sec O o: 210 sec H1: H 0 sec 1: 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.)

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 C is correct.

t = 2.74

p - value = 0.005

Final conclusion: Option A is correct.

What result suggests: Option B is correct.

Mean Sample Mean Std. Err. DF T-Stat P-value 235.1 9.1547938 39 2.741733 0.0046

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