static assignment

Homework 7 – Due Monday, November 16 at 11:59PM1.[4pt]

Do problem 7.22 on p 266 of theOpenIntrotextbook.2.[4pt]Do problem 6.34 on p 239 of theOpenIntrotextbook.3. Thed1dataset was taken from theSleuth3package inR. Here is the description:Are any physiological indicators associated with schizophrenia? In a 1990article, researchers reported the results of a study that controlled for genetic andsocioeconomic differences by examining15pairs of monozygotic twins, where oneof the twins was schizophrenic and the other was not. The researchers usedmagnetic resonance imaging to measure the volumes (in cm3) of several regionsand subregions of the twins’ brains.You can access the volumes of the Affected group withd1$Volume[d1$Group == “Affected”]You can access the volumes of the Unaffected group withd1$Volume[d1$Group == “Unaffected”](a)[1pt]Suppose your test’s independence assumption holds. Draw the appropriatehistogram or histograms to determine if the normality condition is met. If thehistogram(s) doesn’t look normal, does the Central Limit Theorem apply?(b)[1pt]Perform the appropriatet-test to determine if there is a difference in mean brainvolume between the Unaffected and Affected groups. Report:i. Thet-statisticii. The degrees of freedomiii. The p-value(c)[1pt]What do you conclude at the0.05significance level?(d)[1pt]Report the confidence interval. Based on this interval, are we95%confident thatone group has a larger mean brain volume? If so, which?

4. Thed2dataset was taken from theopenintropackage inR. It contains personal incomesfor175people from California and212people from Ohio.You can access the incomes of the California group withd2$personal_income[d2$state == “California”]You can access the incomes of the Ohio group withd2$personal_income[d2$state == “Ohio”](a)[1pt]Suppose your test’s independence assumption holds. Draw the appropriatehistogram or histograms to determine if the normality condition is met. If thehistogram(s) doesn’t look normal, does the Central Limit Theorem apply?(b)[1pt]Perform the appropriatet-test to determine if the mean personal income inCalifornia is greater than the mean personal income in Ohio. Report:i. Thet-statisticii. The degrees of freedomiii. The p-value(c)[1pt]What do you conclude at the0.05significance level?