Question

(c) find the standardized test statistic.
the standardized test statistic is t = 0.19.
(round to two decimal places as needed.)
(d) decide whether to reject or fail to reject the null hypothesis.
fail to reject h₀ because the standardized test statistic is not in the rejection region.
(e) interpret the decision in the context of the original claim.
there is not enough evidence at the 10% level of significance to support the claim that the mean amount of carbon monoxide in the air in u.s. cities is 2.34 parts per million.
(type integers or decimals. do not round.)

Explanation:

Step1: Identify Test Type

The problem involves a standardized test statistic (t - statistic here, rounded to 0.19) and hypothesis testing. We need to check if the test statistic lies in the rejection region. For a significance level (let's assume two - tailed or one - tailed, but from the context, likely two - tailed or a specific tail). The rejection region is the area where we reject the null hypothesis.

Step2: Compare Statistic to Rejection Region

The standardized test statistic \(t = 0.19\). If we consider the rejection regions (the shaded areas in the graphs), we check if \(0.19\) is in the shaded (rejection) area. From the given information, it says the test statistic is not in the rejection region. So, we fail to reject the null hypothesis.

Step3: Interpret the Decision

In the context of the claim (about the mean amount of carbon monoxide in US cities), since we fail to reject the null hypothesis, there is not enough evidence at the 10% level of significance to support the claim.

Answer:

• (c) The standardized test statistic \(t = 0.19\) (rounded to two decimal places).
• (d) Fail to reject \(H_0\) because the standardized test statistic is not in the rejection region.
• (e) There is not enough evidence at the 10% level of significance to support the claim that the mean amount of carbon monoxide in the air in US cities is [the claimed value, likely related to 2.34 parts per million].