Question

listed below are the lead concentrations (in μg/g) measured in different ayurveda medicines. ayurveda is a traditional medical system commonly used in india. the lead concentrations listed here are from medicines manufactured in the united states. assume that a simple random sample has been selected. use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14.0 μg/g.
2.98 6.54 5.96 5.50 20.50 7.52 12.04 20.51 11.52 17.52
h₀: μ = 14.0
h₁: μ < 14.0
(type integers or decimals. do not round.)
identify the test statistic.
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the sample mean \(\bar{x}\)

$$ \bar{x}=\frac{2.98 + 6.54+5.96+5.50+20.50+7.52+12.04+20.51+11.52+17.52}{10}=\frac{110.09}{10}=11.009 $$

Step2: Calculate the sample standard deviation \(s\)

$$
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$$

$$
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$$

$$ s=\sqrt{\frac{376.4377}{9}}\approx6.46 $$

Step3: Calculate the test statistic \(t\)

The formula for the \(t\) - test statistic in a one - sample \(t\) - test is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\), where \(\mu = 14.0\), \(\bar{x}=11.009\), \(s\approx6.46\), and \(n = 10\)

$$ t=\frac{11.009-14.0}{6.46/\sqrt{10}}=\frac{- 2.991}{2.043}\approx - 1.46 $$

Answer:

\(-1.46\)