Question

In trying to determine whether air pollution causes reduction in children's lung health a researcher proposes to see if the lung volume of 10-year-old boys who live in high ozone pollution is significantly less than the lung volume of all 10-year-old boys. The mean volume for all 10-year-old boys is 2.05 liters. A random sample of 26 10-year-old boys who live in a community with high levels of ozone pollution is found to have a mean volume of 1.98 liters, with a sample standard deviation of 0.3 liters. Test the researcher's claim that the mean lung volume of 10 -year-old boys who live in a community with high levels of ozone pollution is less than 2.05 at the 5% significance level.

Answer 1

The test statistic will be "-2.33". A further explanation is provided below.

Explanation:

According to the question,

`H_0: \mu = 2.05`

`H_0: \mu < 2.05`

Given:

`\bar x = 1.98`

`s = 0.3`

`n = 100`

The test statistics will be:

⇒
`t_0 = (\bar x - \mu_0)/((s)/(√(n) ) )`

`=(1.98-2.05)/((0.3)/(√(100) ) )`

`=-2.33`

and the P-value will be:

=
`0.011< \alpha`