help me to prove those 2 questions

The following R outputs may or may not be useful. For the non-R problems, do not use your own code.

pnorm(.025)=0.5099725

pnorm(-21.4374)=2.993311e-102, pnorm(-22.2587)=4.645122e-110

qnorm(.025)=-1.959964

pt(.2905,df=19)=.6127096, pt(.2905,df=9)=.6109918

pt(2.8838,df=19)=.9952445, pt(2.8838,df=9)=.9909671

pt(.025,df=375)=.5099659, pt(.025,df=103)=.5099483, pt(.025,df=271)=.5099633

pt(-6.2885,df=375)=4.463317e-10, pt(-6.2885,df=103)=3.928565e-09

pt(-6.2885,df=271)=6.392422e-10

qt(.025,df=375)=-1.96631, qt(.025,df=103)=-1.983264, qt(.025,df=271)=-1.968756

10.54

internet book prices Annas project for her introductory statistics course was to compare the selling prices of textbooks at two Internet bookstores. She first took a random sample of 10 textbooks used that term in courses at her college, based on the list of texts compiled by the college bookstore. The prices of those textbooks at two Internet sites were Site A: $115, $79, $43, $140, $99, $30, $80, $99, $119, $69

SiteB: $110,$79,$40,$129,$99,$30,$69,$99,$109,$66 (a) Test at the .1 level whether the population mean prices at the two sites are different. Show all steps and interpret the conclusion for full credit. The following R output may or may not be useful.

> priceA=c(115,79,43,140,99,30,80,99,119,69)

> priceB=c(110,79,40,129,99,30,69,99,109,66)

> mean(priceA)

[1] 87.3

> mean(priceB)

[1] 83

> sd(priceA)

[1] 34.19893

> sd(priceB)

[1] 31.95831

> sd(priceA-priceB)

[1] 4.715224

(b) Multiple choices: Based on your answer to (a), which interval most likely describes the 90% confidence interval for the mean difference between book prices at site A vs. those at site B, i.e., A-B? Explain.

I II III

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0

A. Interval I

B. Interval II

C. Interval III

D. There is not enough information to tell. We need to do calculation.

10.92

a danish study of individuals born at a copenhagen hospital between 1959 and 1961 reported higher mean IQ scores for adults who were breast-fed for longer lengths of time as babies (E. mortensen et al., mama, vol. 287, 2002, pp. 2365-2371). the mean iq score was 98.1(s=15.9) for the 272 subjects who had been breast-fed for no longer than a month and 108.2 (s=13.1) for the 104 subjects who had been breast-fed for seven to nine months.

(a) Identify the response variable and explanatory variable. Indicate whether each variable is quantitative or categorical.

(b) Calculate and interpret the 95% confidence interval shown for the difference in IQ score between the two groups.

(c) What assumptions must you make for the confidence interval in (b) to be valid?

(d) Test at the 0.05 level whether the babies breastfed for longer have higher IQs. You only need to show how to find the test statistic and p-value.

(e) Interpret the p-value you calculated in (d).

(f) Can you conclude that breast-feeding helps IQ? Explain.