Question

Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5 < u < 13.1 with a 95% level of confidence when o is known. (1) Find the point estimates for the unknown population mean. (ii) Find the margin of error. (iii) Give the interpretation of the confidence interval. (iv) Name two ways of decreasing the width of the confidence interval. b) State the assumptions necessary for linear regression model Y = A + Bx + E c) Let o be a sample proportion based on a random sample of size n from a binomial distribution with unknown p, such that yộ > 5 and yq > 5. Construct a (1 - a)100% confidence interval for the unknown population proportion p using Ộ N(uộ = p, oộ= V p)

Answer 1

Heae.., 0:05 Upper limit Question: 120. The.954. confidence interval for true population mean when is known is given by (3:5 <l< 13:1). Q = la confidence level = 2x12 - 1.96 lower limit z û - E û - E = 3:5 û + E :-:13:1 where Û = point estimate of population medo margin of ever i). The point estimation of population mean is given by û = ( Lower limit + Upper limit) -2.1 (-3.5: 13.1) 2 E 8:37 jij Margin of eesooo (E) low ez limit sei - E= 3-5 E ů - 3.5 + 8. 3-13.5 4.8 iii) Ipteopoetation ! We are 954. confident that the toue population mean will lies between C 3.5 and 13:00) iv) a) incoease the sample size (1) b) decoease the confidence level

model Il b) The necessary assumption foo linear regression Y-A7 Baze te is follows. i) Linearity: The relationship between x and x mean of y should be linear. 3) Homoscedasticity ; The variance of residual is constant fog ony value of x. jis Independence. Each obsenations are independent to each other. iv). Normality. The foo any value of x and y should be normally dista'buted. c) The 100(1-4) p. :confidence interval for the unknown population propolation is given by P (1213 Za12) = d. ř TZT$ 20/12) 2012) = 1-0. undeo 6-8 VPN > pet g-pl< Zoal2 ypx = 14 > p (p - 2012 - BV R< $+ Zuby Pyard Replace pv - Øv PC -P. & Lar2 -0. => pfẾ -2412. V < p < pit dem ex ):1-6 Thus, (1-a) 100 f. confidence internal for population proportion is glven by (6 - W2 A Laya yeye a t