Mathematics, 04.12.2019 07:31, NLMB2614

Arandom sample of n1 = 49 measurements from a population with population standard deviation σ1 = 3 had a sample mean of x1 = 12. an independent random sample of n2 = 64 measurements from a second population with population standard deviation σ2 = 4 had a sample mean of x2 = 14. test the claim that the population means are different. use level of significance 0.01.what distribution does the sample test statistic follow? explain.

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We reject the null hypothesis that the population means are equal and accept the alternative hypothesis that the population means are different.

Step-by-step explanation:

We have large sample sizes $n_{1} = 49$ and $n_{2} = 64$ , the unbiased point estimate for $\mu_{1}-\mu_{2}$ is $\bar{x}_{1} - \bar{x}_{2}$ , i.e., 12-14 = -2.

The standard error is given by $\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}$ , i.e.,

$\sqrt{\frac{(3)^{2}}{49}+\frac{(4)^{2}}{64}}$ = 0.6585.

We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative). The rejection region is given by RR = {z | z < -2.5758 or z > 2.5758} where -2.5758 and 2.5758 are the 0.5th and 99.5th quantiles of the standard normal distribution respectively. The test statistic is $Z = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{\sqrt{\frac{\sigma^{2}_{1}}{n_{1}}+\frac{\sigma^{2}_{2}}{n_{2}}}}$ and the observed value is $z_{0} = \frac{-2}{0.6585} = -3.0372$ . Because -3.0372 fall inside RR, we reject the null hypothesis.

The test statistic follow a standard normal distribution because we are dealing with large sample sizes.

answered: Guest

answer: segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students. an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality. in the case of brown v. board of education, that standard was challenged and defeated. segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to education. this was being violated by states whose laws supported the segregation of schools. section 1 of the 14th amendment reads as follows:

all persons born or naturalized in the united states and subject to the jurisdiction thereof, are citizens of the united states and of the state wherein they reside. no state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the united states; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.

answered: Guest

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