Assume that a simple random sample has been selected from a normally distributed
ID: 3269107 • Letter: A
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
218.0
sec and a standard deviation of
One-Sample T
muequals=210
greater than>210
95% Lower
N
Mean
StDev
SE Mean
Bound
T
P
40
218.00
55.15
8.72
203.31
0.92
0.182
55.15
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
One-Sample T
Test ofmuequals=210
vsgreater than>210
95% Lower
N
Mean
StDev
SE Mean
Bound
T
P
40
218.00
55.15
8.72
203.31
0.92
0.182
Explanation / Answer
Since P value 0.182 is greater than 0.05, we failed to reject the null hypothesis and conclude that there is not sufficient evidence that mean is greater than 210
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