Aschool teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pci/l. the school samples the air for 36 days and finds an average concentration of 4.4pci/l with a standard deviation of 1pci/l. at a 5% significance level, the critical value(s) is (are)

At a 5% significance level, the critical value is 1.690.

Step-by-step explanation:

Let denotes the average concentration of radon gas.

Given : A school teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.

As per given , the appropriate hypothesis to test :

[Note : Alternative hypothesis used to express strictly greater than or less than signs and null hypothesis is opposite of it.]

∵ alternative hypothesis is right tailed , so the test must be a right tailed test (one-tailed test.)

Also the population standard deviation is unknown , so we use t-test.

[Note : we have given sample standard deviation as s=1pCi/L. ]

Sample size : 36

Then , degree of freedom = n-1=35

Now, for level of significance, the right-tailed critical value would be

     [Using the students' t-distribution table ]

Hence, At a 5% significance level, the critical value is .

9 x 8 divided by (5-3)=36