Question

the claim is that smokers have a mean cotinine level greater than the level of 2.04 ng/ml found for nonsmokers (cotinine is used as a biomarker for exposure to nicotine ) the sample size is n = 825 and the test statistic is t = 57.090. use technology to find the p - value based on the result, what is the final conclusion? use a significance level of 0.01
state the null and alternative hypotheses.
h₀: μ = 2.84
h₁: μ > 2.84
(type integers or decimals do not round )
the test statistic is 57.10
(round to two decimal places as needed )
the p - value is 0.000
(round to three decimal places as needed )
based on the p - value, there sufficient evidence at a significance level of 0.01 to the claim that smokers have a mean cotinine level greater than the level of 2.84 ng/ml found for nonsmokers

Explanation:

Step1: Hypothesis testing concept

In hypothesis testing, if the \(P -\) value \(\leq\) significance level (\(\alpha\)), we reject the null hypothesis.

Step2: Compare \(P -\) value and \(\alpha\)

Here, the significance level \(\alpha = 0.01\) and the \(P -\) value \(= 0.000\). Since \(0.000<0.01\) (i.e., \(P -\) value \(\leq\alpha\)).

Step3: Conclusion

We reject the null hypothesis \(H_0:\mu = 2.84\). So, there is sufficient evidence to support the alternative hypothesis \(H_1:\mu> 2.84\), which means there is sufficient evidence at a significance level of \(0.01\) to support the claim that smokers have a mean cotinine level greater than \(2.84\) ng/mL.

Answer:

There is sufficient evidence at a significance level of \(0.01\) to support the claim that smokers have a mean cotinine level greater than the level of \(2.84\) ng/mL found for nonsmokers.