# Hypothesis Testing of Mean

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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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 = 0.05

Rejection criteria: Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value at the 0.05 significance level.

Upper critical value = 1.644853627

Conclusion: Reject the null hypothesis, since the calculated value of test statistic is greater than the critical value. The sample provides enough evidence to support the claim that the average age of European soccer players has increased significantly.

Details

Z Test of Hypothesis for the Mean

Data

Null Hypothesis = 26

Level of Significance 0.05

Population Standard Deviation 4

Sample Size 81

Sample Mean 27

Intermediate Calculations

Standard Error of the Mean 0.444444444

Z Test Statistic 2.25

Upper-Tail Test

Upper Critical Value 1.644853627

p-Value 0.012224473

Reject the null hypothesis

When significance level, α = 0.01

Rejection criteria: Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value at the 0.01 significance level.

Upper critical value = 2.326347874

Conclusion: Fails to reject the null hypothesis, since the calculated value of test statistic is less than the critical value. The sample does not provide enough evidence to support the claim that the average age of European soccer players has increased significantly.

Details

Z Test of Hypothesis for the Mean

Data

Null Hypothesis = 26

Level of Significance 0.01

Population Standard Deviation 4

Sample Size 81

Sample Mean 27

Intermediate Calculations

Standard Error of the Mean 0.444444444

Z Test Statistic 2.25

Upper-Tail Test

Upper Critical Value 2.326347874

p-Value 0.012224473

Do not reject the null hypothesis

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