Question

Q12. a) Suppose the given confidence interval estimates the true population mean as 3.5<μ<13.1 with a 95% level of confidence when σ is known.

(i) 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+ε

c) Let p^ be a sample proportion based on a random sample of size n from a binomial distribution with unknown pp, such that γp^>5 and γq>5.

Construct a (1−α)100% confidence interval for the unknown population proportion

p using p^≈N

(μp^=pp^≈N(μp^=p, σp^=PVn−−−√)

Answer 1

Given, (1-4) 100 = 95 I-a -95 100 | - = 0.gs 2= 1-0.95 a=005 il The point estimates for the unknown population mean. is 3.5 < < 13.) Ž = 3.5+ 13.1 2 = 8.30 ... The point estimates for the Unknown population mean is 8.30 of error is, The margin confidence interval for estimating Population mean with o known CI = 7+ E CSScanned with CamScanner

E = 2 ( 0 ) X + upper limit - 13. 1 = 8.30 + E E = 1351 - 836 E = 4.80 ... The margin of of error .is 4.80 (iii) We estimate with 95% contidence that the true value of the population mean is between 3.5 and 13.1 civ) Two ways to reduce the width of o confidence intervalg are, organers ample_Size and lowe wer level of contidence CScanned with CamScanner

E = 2 ( 0 ) X + upper limit - 13. 1 = 8.30 + E E = 1351 - 836 E = 4.80 ... The margin of of error .is 4.80 (iii) We estimate with 95% contidence that the true value of the population mean is between 3.5 and 13.1 civ) Two ways to reduce the width of o confidence intervalg are, organers ample_Size and lowe wer level of contidence CScanned with CamScanner