Answer:
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.
Step-by-step explanation:
1) Data given and notation
represent the mean age when smokers first start to smoke varies
represent the standard deviation for the sample
represent the population standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t 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 determine if the mean starting age is at least 19, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:
(1)
z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".
Calculate the statistic
We can replace in formula (1) the info given like this:
Calculate the P-value
Since is a one-side lower test the p value would be:
Conclusion
If we compare the p value and the significance level given for example we see that
so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.