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Answer:
When we compare the significance level we see that
so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.
Step-by-step explanation:
Data given and notation
represent the sample mean
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the average age of the evening students is significantly different from 21, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Calculate the statistic
We can replace in formula (1) the info given like this:
P-value
Since is a two sided test the p value would be:
Conclusion
When we compare the significance level we see that
so we can reject the null hypothesis at 10% of significance. So the the true mean is difference from 21 at this significance level.