Question

listed below are the lead concentrations (in μg/g) measured in different ayurveda medicines. ayurveda is medical system commonly used in india. the lead concentrations listed here are from medicines manufac united states. assume that a simple random sample has been selected. use a 0.10 significance level to t that the mean lead concentration for all such medicines is less than 14.0 μg/g. 3.02 6.46 6.02 5.52 20.52 7.49 11.96 20.52 11.51 17.53 identify the null and alternative hypotheses. h₀: μ = 14.0 h₁: μ < 14.0 (type integers or decimals. do not round.) identify the test statistic. -1.44 (round to two decimal places as needed.) identify the p - value. (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The sample size \(n = 10\). The degrees of freedom \(df=n - 1=10 - 1 = 9\)

Step2: Use the t - distribution table or calculator

We have a one - tailed test (since \(H_1:\mu<14.0\)) and the test statistic \(t=-1.44\) with \(df = 9\).
Using a t - distribution calculator or table for a one - tailed test with \(t=-1.44\) and \(df = 9\)
The p - value is the probability of getting a value as extreme or more extreme than the test statistic.
For a t - distribution with \(df = 9\) and \(t=-1.44\) (one - tailed), using a calculator (e.g., in R: pt(-1.44,9) or in Excel: T.DIST(-1.44,9,TRUE)), we find the p - value.

Answer:

\(0.092\)