Question

i need help with 5 & 6

5. A gerentologist is studying whether Medicare patients receive the same attention from doctors as senior citizens with other insurance. She decides to measure this by average length of a preventative care visit. In the data she collects, 44 Medicare patients saw the doctor for a mean time of 18.72 minutes, with a standard deviation of 5.16 minutes, while 33 seniors with other insurance had a mean visit of 21.12 minutes, with a standard deviation of 6.17 minutes. a. Under the assumption of equal (population) variances, find a 98% confidence interval for the difference in visit length between the underlying groups. b. Given that population variances are not assumed equal, determine the degrees of freedom for the precise model, and find a 98% confidence interval for the difference in visit length. c. What conclusion should she reach based on each of these confidence intervals? 6. It is claimed that students in MATH 2111 fare differently based on whether they took Calculus in the previous semester or before that. In random samples of 31 students who had Calculus in the previous term and 24 students who did not, 19 students in the first group get a high grade (Bor better), as do 11 in the second. a. Using the conservative model, find a 95% confidence interval for the difference in the proportion of high grades. b. What does this say about the claim?

Answer 1

Question 5 we have given: Her X, = medicore patients. ng = sample size = 44, z, = sample mean = 18.72 € S, = sample standard devichon = 5:16. R2 = senior citizen with other insurance nz: sample size = 33, z = sample mean = 21.12 ď sa sample standard deviahon = 6:17 a) Assume equul the difference for vorrianie in visit 98% confidence internal length between ... the underlying groups.

df = degree of freedom - n, the-2 = 44 +33-21=75 itd 12. dr +2.377 / (from feble) (H, -2) = ( (az - Az) † (tallar df + 2 +S? 37 srl 1872- 21:12) (2.377 * (S 16)2 33 =(-2.4 + 3.15 23) = (-5:5523, 07523) we can say qoi confident that difference between

population mean is lies within above interval b) popn variances asome not equa. of= Le) +($ hirl 5 .16 ) - [ Sesve to contingent 33 = 3.09313 (0.008515+ 0.04158] ( 6:17 44 33 32

12 [[ 61.7452 & 62 .. tala, df = to.02,62 € 2.388-cfrom febles = [-2.4 † (2-3884 1.3261)] = (-2-4 + 3.1668] = (-5.5668, 0.7668] we can say 981. Confident that difference between population mean is lies within 5.56888 to 0.7858

© for each conkidence internal conclusion is not significant because each have include null value. © we have: n= 31 NE 24, - 91=19 & 92=11. 1:29 - Se Regno E0-6129] P = y 30-4583] claim :- It is claimed that students in Math all fare differently based on whether they rook calculus in the previous semister or before that

a) ce, -Pad ECCEA B) † (20121* JECO +242) 2.3212= zoos E 11.967 (from table) - [10.6129 -0.4583) + (1-964 (0.612980-387)+60.45840.54) 24 llz80100 +689400:05 * 90:1) F 9h31-0] = [et anklio * 90.1) F ghslio) = [6292.0 I ansio ] (Ethio' 180110- ) 3

we can say 95% confident that the difference of high grades is lies within in the proportion -0.1081 to 0.4173. o actually result or Internal is not significant if it include any null value here Interval include null value hence it is not significant .& our claim not satisfy here.