Hypothesis Testing of Mean
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Historically the average age of European soccer players is reported as 26 years with a standard deviation of 4 years. A random sample of 81 European professional soccer players has an average age of 27 years. We would like to decide if there is enough evidence to establish that average age of European soccer players has increased significantly. What is the decision at ?=.05 and 0.01? Indicate which test you are performing; show the hypotheses, the test statistic and the critical values and mention whether one-tailed or two-tailed.
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Solution Summary
Hypothesis Testing of Mean for European soccer.
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Answer
Since the population standard deviation is known, we can use z test for mean.
We are testing whether the average age of European soccer players has increased significantly. Hence the test is one-tailed and is an upper tailed test.
The null hypothesis tested is
H0: Average age of European soccer players ≤ 26 years. (µ ≤ 26)
The alternative hypothesis is
H1: Average age of European soccer players > 26 years. (µ > 26)
The test statistic used is , where =27, n = 81, = 4
Therefore, = 2.25
When significance level, α = ...
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