OPRE 3360 Exam 2 Questions With Correct Marking Scheme

OPRE 3360 Exam 2 Questions With Correct Marking Scheme /.sample variance (σ^2) - Answer-(Xi - sample mean)^2 / (n-1) /.sample proportion (p bar) - Answer-Xi: 0,1 responses /.p bar - Answer-sum of mean of all responses/n /.sample error - Answer-sample statistic - true population value x̄ - μ p bar - p /.right skewed (positively skewed) - Answer--long right tail -large weight on the left -median mean /.Xi ~ N (nμ, sqrt(n)σ) - Answer-ex: mean= 800 n= 40 std dev= 600 what is prob that ______ is = 40,000 N(40x800, sqrt(40) x 600)= N(32000, 3795) (40,000, 32,000, 3795, 1) /.sample mean x̄ - Answer-sum/n ~ N(μ, σ/sqrt(n) /.sampling error - Answer-~ N(0, σ/sqrt(n)) /.standard sampling error - Answer-(x̄-μ) / (σ- sqrt(n)) ~ N(0,1) /.sample proportion - Answer-special case of sample mean p bar= # of yes / n Xi= 1(yes), 0(n) μ= E[Xi] = p Var[Xi]= p(1-p) σ = sqrt(p(1-p)) p bar~ N(p, sqrt(p(1-p)/n) p(p bar = #) = p(z = #-p/p bar) n= 30 np= 5, n(1-p)= 5 /.biggest mistake by AIG - Answer-assumed that the individual CDS were independent business model for insurance companies entirely depends on the CLT /.point estimate - Answer-single # computed from sample: x bar or p bar /.confidence interval - Answer-point estimate -+ margin of error /.confidence lvl - Answer-(1-α) -how likely (in repeated trial sense) the interval contains the true value of the parameter in % ex: 1-α= .9 (90% confidence) -determines critical value: # of std errors to be included in a margin of error /.confidence interval generic formula: - Answer-point estimate -+ (crit value)(standard error) -critical value determined by the sampling distribution of standardized sampling error (z-dist or t-dist) & confidence lvl /.Target parameters and corresponding formulas - Answer-mean μ σ known: o sample size- n= 30 OR normal dist o stdev of indiv observation- σ o std error- σ/√n o critical value- Z mean μ σ unknown: o sample size: n= 30 or normal o stdev of indiv observation- S o std error- s/√n o crit value- t d.f.=n-1 proportion p: o n=30, np=5, n(1-p)=5 o stdev of indiv observation- √(p(1-p)) o std error- √((()/n)) ~whole thing sqrt o crit value- Z /.mean μ σ known: - Answer- -+ (crit z)(σ/√n) step 1: consider confidence lvl % step2: 1-confidence lvl= α α/2 step 3: (α/2)= critical Z value /.95% of sample mean: - Answer-w/in -+1.96 std errors from the mean if we add or sub 1.96 std errors we capture the mean 95% of the time /.common confidence lvls - Answer-90% - confidence coefficient (1-α): .9 - crit z value: 1.645 95% - confidence coefficient (1-α): .95 - crit z value: 1.96 99% -confidence coefficient (1-α): .99 - crit z value: 2.57 /.critical value ^ w/ ^ confidence lvl - Answer- /.The higher the confidence level... - Answer-the wider the confidence interval (more forgiving) -margin of error should increase /.margin of error: (crit value)(std err) - Answer--amt added and subtracted to the point estimate margin of err increases as σ increases margin of err decreases as n ^ m.e. ^ as confidence lvl ^ /.how to make margin of err no greater than certain lvl - Answer-m.e. = Z (σ/√n) m.e.^2 = Z^2 (σ^2/n) n= Z^2 (σ^2/m.e.^2) (round up!!) /.mean μ σ unknown - Answer- -+ (crit t)(s/√n) step 1: consider confidence lvl % step2: 1-confidence lvl= α α/2 step 3: .2t(α,d.f.)= critical t value