Question

the iq scores for a random sample of subjects with low lead levels in their blood and another random sample of subjects with high lead levels in their blood were collected. the statistics are summarized in the accompanying table. assume that the two samples are independent random samples selected from normally distributed populations. do not assume that the population standard deviations are equal. complete parts (a) to (c).

1. use a 0.05 significance level to test the claim that the mean iq score of people with low blood lead levels is higher than the mean iq score of people with high blood levels.

what are the null and alternative hypotheses? assume that population 1 consists of subjects with low lead levels and population 2 consists of subjects with high lead levels.

a. ( h_0: mu_1 = mu_2 ) ( h_1: mu_1 > mu_2 )
b. ( h_0: mu_1
eq mu_2 ) ( h_1: mu_1 > mu_2 )
c. ( h_0: mu_1 = mu_2 ) ( h_1: mu_1
eq mu_2 )
d. ( h_0: mu_1 leq mu_2 ) ( h_1: mu_1 > mu_2 )

	low lead level ( mu_1 )	high lead level ( mu_2 )
( \bar{x} )	91.81392	86.41874
( s )	15.55108	8.48375

Explanation:

The claim is that the mean IQ score of people with low lead levels ($\mu_1$) is higher than that of people with high lead levels ($\mu_2$). The null hypothesis ($H_0$) is a statement of equality or no difference, and the alternative hypothesis ($H_1$) reflects the claim. So $H_0: \mu_1 \leq \mu_2$ (since we test against the claim, the null is the opposite or equality) and $H_1: \mu_1 > \mu_2$, which matches option D.

Answer:

D. $H_0: \mu_1 \leq \mu_2$, $H_1: \mu_1 > \mu_2$