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Answer: At a 5% significance level, the critical value is <u>1.690</u>.
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 .