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). (a) write the claim mathematically and identify \\( h_0 \\) and \\( h_a \\). choose from the following. a. \\( h_0: \mu < 32 \\) \\( h_a: \mu \geq 32 \\) (claim) b. \\( h_0: \mu \leq 32 \\) \\( h_a: \mu > 32 \\) (claim) c. \\( h_0: \mu \geq 32 \\) (claim) \\( h_a: \mu < 32 \\) d. \\( h_0: \mu = 32 \\) (claim) \\( h_a: \mu > 32 \\) e. \\( h_0: \mu = 32 \\) \\( h_a: \mu > 32 \\) (claim) f. \\( h_0: \mu \leq 32 \\) (claim) \\( h_a: \mu > 32 \\)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or non - difference, and the alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. The scientist's claim is that the mean nitrogen dioxide level \(\mu>32\). The null hypothesis is the opposite of the alternative hypothesis for a one - tailed test. So, \(H_0:\mu\leq32\) (the status - quo or opposite of the claim) and \(H_a:\mu > 32\) (the claim).

Answer:

B. \(H_0:\mu\leq32\), \(H_a:\mu > 32\) (claim)