Question

Nitrogen dioxide (NO2) is toxic by inhalation. A scientist claims that the population mean nitrogen dioxide level in West London is higher than 30 parts per billion and collects the NO2 levels for 36 randomly selected days. The results show an average of 32.86 and the standard deviation of 12.72 parts per billion. Historical data show that the nitrogen dioxide levels follow a normal distribution with a standard deviation of 12 parts per billion.

(a) (3 pts) Construct a 95% confidence interval for the population mean nitrogen dioxide level in West London.

(b) (7 pts) Test if there is significant evidence for the scientist’s claim given the level of significance 5%. Show all steps of a hypothesis testing.

(c) (2 pts) Can you use the result in part (a) for the test in part (b)? Justify your answer.

Answer 1

Given:

n = 36, = 32.86, Standard deviation (S) = 12.72 , Population standard deviation () = 12

Critical value:

Z_/2 = Z _0.05/2 = 1.96

a) Construct 95% Confidence interval:

(28.94 , 36.78)

We are 95% confidence that the population mean is lies in that interval.

b)

Hypothesis:

Ho: = 30 OR The population mean nitrogen dioxide level in West London is 30 parts per billion

Ha: > 30 OR A scientist claims that the population mean nitrogen dioxide level in West London is higher than 30 parts per billion

Test statistic:

Critical value:

Z = Z _0.05 = 1.645

Decision Rule:

Z > Z  , Then Reject Ho at 5% level of significance.

Conclusion:

Here Z < Z, i.e 1.43 < 1.645, That is Fail to Reject Ho at 5% level of significance.

Therefore, The population mean nitrogen dioxide level in West London is 30 parts per billion

C)

in part a) 95% Confidence interval becomes,

(28.94 , 36.78)

Therefore, Population mean = 30 lies in that interval, Therefore, Accept Ho at 5% level of significance.

Therefore, In both parts a & b we conclude that, the population mean nitrogen dioxide level in West London is 30 parts per billion