A sample of 64 observations is selected from a normal population. The sample mean is 215, and the population standard deviation is 15. Conduct the following test of hypothesis using the .03 significance level. What is the p-value?H0 : μ ≥ 220H1 : μ < 220

If we compare the p value and the significance level given we see that then we have enough evidence to conclude that the true mean is significantly lower than 220 at 3% of significance.

Step-by-step explanation:

Data given

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 lower than 220, 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 one-side lower test the p value would be:      

Conclusion      

If we compare the p value and the significance level given we see that then we have enough evidence to conclude that the true mean is significantly lower than 220 at 3% of significance.

square root

step-by-step explanation: