Math / Data & Statistics

QuestionListed below are the lead concentrations (in $\mu \mathrm{g} / \mathrm{g}$ ) 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 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than $14.0 \mu \mathrm{~g} / \mathrm{g}$ . 3.02 6.46 6.00 5.53 20.50 7.47 11.99 20.50 11.53 17.54
Identify the null and alternative hypotheses. $\mathrm{H}_{0}$ : $\square$ $\square$ $\mathrm{H}_{1}$ : $\square$ $\square$ (Type integers or decimals. Do not round.)

Studdy Solution

STEP 1

1. The sample data is a simple random sample from the population.
2. The distribution of lead concentrations is approximately normal or the sample size is large enough for the Central Limit Theorem to apply.
3. We are using a significance level of $\alpha = 0.05$ .

STEP 2

1. Define the null hypothesis ( $H_0$ ).
2. Define the alternative hypothesis ( $H_1$ ).

STEP 3

Define the null hypothesis ( $H_0$ ).
The null hypothesis states that the mean lead concentration for all such medicines is equal to $14.0 \, \mu \mathrm{g/g}$ .
$H_0: \mu = 14.0$

STEP 4

Define the alternative hypothesis ( $H_1$ ).
The alternative hypothesis states that the mean lead concentration for all such medicines is less than $14.0 \, \mu \mathrm{g/g}$ .
$H_1: \mu < 14.0$
The hypotheses are:
$H_0: \mu = 14.0$ $H_1: \mu < 14.0$

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