Question

2. Arsenic is a compound that occurs naturally in very low concentrations. Arsenic blood concentrations in healthy individuals are Normally distributed, with a mean of 3.2 mg/dl and a standard deviation of 1.5 mg/dl. A researcher believes that one area of the United States has naturally elevated arsenic levels in the ground and water supplies. An SRS of 25 individuals in this area found a sample mean arsenic level of 3.75 mg/dl. What are the null and alternative hypotheses for this study?

Answer 1

The null hypothesis
`H_o : \mu = 3.2 \ mg/dl`

The alternative hypothesis
`H_a : \mu > 3.2 \ mg/dl`

Explanation:

From the question we are told that

The mean is
`\mu = 3.2 \ mg/dl`

The standard deviation is
`\sigma = 1.5 mg/dl`

The sample size is n = 25

The sample mean is
`\= x = 3.75 \ mg /dl`

Generally

The null hypothesis is : That the mean of the Arsenic blood concentrations in healthy individuals is
`\mu = 3.2 \ mg/dl`

i.e

The null hypothesis
`H_o : \mu = 3.2 \ mg/dl`

The alternative hypothesis is : That the mean of the Arsenic blood concentrations in healthy individuals is greater than
`\mu = 3.2 \ mg/dl`

The alternative hypothesis
`H_a : \mu > 3.2 \ mg/dl`