Question

test a claim that the mean amount of carbon monoxide in the air in u.s. cities is less than 2.32 parts per million. it was found that the mean amount of carbon monoxide in the air for the random sample of 65 cities is 2.38 parts per million and the standard deviation is 2.11 parts per million. at \\( \alpha=0.01 \\), can the claim be supported? complete parts (a) through (e) below. assume the population is normally distributed.
(a) identify the claim and state \\( h_{0} \\) and \\( h_{a} \\). which of the following correctly states \\( h_{0} \\) and \\( h_{a} \\)?
\\( h_{0}: \mu \geq 2.32 \\)
\\( h_{a}: \mu<2.32 \\)
(type integers or decimals. do not round.)
the claim is the alternative hypothesis.
(b) use technology to find the critical value(s) and identify the rejection region(s).
the critical value(s) is/are \\( t_{0}= \\)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 65\). So \(df=65-1 = 64\).

Step2: Find the critical value using a t - distribution table or technology

For a one - tailed test with \(\alpha=0.01\) and \(df = 64\), using technology (e.g., a TI - 84 Plus calculator: invT(0.01,64)), the critical value \(t_0=- 2.39\)

Answer:

\(t_0=-2.39\)