Question

a scientist estimates that the mean nitrogen dioxide level in a city is greater than 30 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 7. at a = 0.11, can you support the scientists estimate? complete parts (a) through (e)
21 39 40 41 24 22 31 41 35 31 34
42 29 31 18 35 25 19 36 26 26 23
17 26 16 18 23 21 31 17 31
(a) write the claim mathematically and identify ( h_0 ) and ( h_a ). choose from the following
a. ( h_0: mu leq 30 )
( h_a: mu>30 ) (claim)
b. ( h_0: mu leq 30 ) (claim)
( h_a: mu>30 )
c. ( h_0: mu<30 )
( h_a: mu geq 30 ) (claim)
d. ( h_0: mu geq 30 ) (claim)
( h_a: mu<30 )
e. ( h_0: mu = 30 )
( h_a: mu>30 ) (claim)
f. ( h_0: mu = 30 ) (claim)
( h_a: mu>30 )

Explanation:

The claim is that the mean nitrogen dioxide level is greater than 30. In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or non - difference. The alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. If the claim is \(\mu>30\), then the null hypothesis is the opposite of the claim (to start with a statement that can be tested against the data). So \(H_0:\mu\leq30\) and \(H_a:\mu > 30\) (where \(H_a\) is the claim).

Answer:

A. \(H_0:\mu\leq30\), \(H_a:\mu > 30\) (claim)