What are the steps involved in this problem? Can you help? Thank you. Question 3

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What are the steps involved in this problem? Can you help? Thank you.

Question 3: The school district in your City is concerned about possible asbestos problems in buildings in an older high school. They contracted with an engineering firm to take 232 random air samples in the school buildings over a two-day period. The mean sample reading is 0.0095 parts per million, with a standard deviation of 0.0041 parts per million. According to EPA, the indoor asbestos standard is 0.01 parts per million. The firm presents the school district with a report that shows the 90% and 99% confidence interval for the mean sample reading. Interpret the results with reference to whether it is likely that EPA standards are violated. Which confidence interval do you believe is most appropriate to use in this case? Hnt: In calculating confidence intervals, note that population standard deviation is unknown

Explanation / Answer

Ans:

As,population standard dviation is unknown,so we will use t multiplier.

sample size=232

df=232-1=231

t multiplier for 90% and 99% confidence interval are 1.651 and 2.597 respectively.

90% confidence interval for mean

=0.0095+/-1.651*0.0041/sqrt(232)

=0.0095+/-0.0004

=(0.0091,0.0099)

99% confidence interval for mean

=0.0095+/-2.597*0.0041/sqrt(232)

=0.0095+/-0.0007

=(0.0088,0.0102)

If we use 90% CI,then EPA standard will be violated as upper limit is less than equal to 0.0099,but if we use 99% CI,then EPA standard will not be violated as CI includes 0.01 within it.

So,using 99% CI is more appropriate.

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