A random sample of 10 college students was drawn from a large university. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24 years, with a sample standard deviation of 3.2. Suppose that you want to test whether the population mean age differs from 20. What is your decision based on a test at a 1% significance level

Solution :

Given :

The sample mean = 21.3

Standard deviation = 3.2

The null hypothesis is :

The alternate hypothesis :

This is a two tailed test, for which a with an unknown population of a standard deviation is being used.

Now the significance level, , as well as the critical value for a two tailed test is

The rejection region is

The t-statistic is computed as follows :

 = 1.285

Since it is observed that , it is then concluded that  

The p-value is p=0.231 and since p 0.231 ≥ 0.1, it is concluded that

Conclusion

Thus we concluded that is not rejected. Therefore, the population mean is different than 20, at the 0.1 significance level.

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