Question

a scientist estimates that the mean nitrogen dioxide level in a city is greater than 32 parts per billion. to test this estimate, you determine the nitrogen dioxide levels for 31 randomly selected days. the results (in parts per billion) are listed to the right. assume that the population standard deviation is 8. at \\( \alpha=0.07 \\), can you support the scientists estimate? complete parts (a) through (e).

(b) find the critical value and identify the rejection region.

\\( z_{0}=1.48 \\) (round to two decimal places as needed.)

rejection region: \\( z>1.48 \\)

(c) find the standardized test statistic.

\\( z=-3.37 \\) (round to two decimal places as needed.)

(d) decide whether to reject or fail to reject the null hypothesis.

reject \\( h_{0} \\)

fail to reject \\( h_{0} \\)

(e) interpret the decision in the context of the original claim.

at the 7% significance level, there enough evidence to the scientists claim that the mean nitrogen dioxide level in the city is greater than 32 parts per billion

Explanation:

Step1: Recall the decision rule

In a hypothesis test, if the standardized test statistic \(z\) falls within the rejection region, we reject the null hypothesis \(H_0\). If it does not, we fail to reject \(H_0\). The rejection region here is \(z> 1.48\).

Step2: Compare the test - statistic with the rejection region

The standardized test statistic \(z=-3.37\). Since \(-3.37<1.48\) (i.e., the test statistic does not fall within the rejection region \(z > 1.48\)).

Answer:

At the \(7\%\) significance level, there is not enough evidence to support the scientist's claim that the mean nitrogen dioxide level in the city is greater than \(32\) parts per billion.