Answer:
We can see that so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly less than 21 at 10% of signficance.
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 true mean is less than 21 or no, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and 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 left side test the p value would be:
Conclusion
We can see that so we can conclude that we have enough evidence to reject the null hypothesis, and the true mean is significantly less than 21 at 10% of signficance.