39. Historically the average age of European soccer players is reported as 26 ye

Question

39.

Historically the average age of European soccer players is reported as 26 years with a standard deviation of 4 years and is assumed to be normally distributed. 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 a=.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. (Ch9)

Explanation / Answer

It is one-tailed test.

The test hypothesis is
Ho:=26
Ha:>26

The test statistic is

Z=(xbar-)/(s/n)

=(27-26)/(4/9)

=2.25

Given a=0.05, the critical value is |Z(0.05)|=1.645 (check standard normal table)

Since 2.25 is larger than 1.645, we reject Ho.

Given a=0.01, the critical value is |Z(0.01)|=2.33 (check standard normal table)

Since 2.25 is less than 2.33, we do not reject Ho.

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