Question

benzene, a chemical used to synthesize plastic, has been labeled as possible cancer causing agent.thirty air samples from a steel manufacturing plant collected over the period of one month, have been examined for benzene content, yielding a sample mean of 1,24 ppm and a sample standard deviation of 0,8 ppm. it is known that the government has lowered the maximum mean benzene level tp 1 ppm.

a)Use one-sided hypothesis test (α= 0,01) to determine whether the mean benzene level of the factory exceeds 1ppm, as data suggests.

b)Compute a 99% confidence interval for the benzene level variance.

write the hypothesis you chose

Answer 1

Here, we are to test,


We use the test statistic:


We reject   at 1% level of significance, iff


The given information are:




Hence,


Now,


We observe that,


Hence, we fail to reject at 1% level of significance and conclude that, the mean benzene level of the factory does not exceed 1ppm.


The 99% confidence interval for the benzene level variance is given by:

Putting in the values, we get,



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