Question

A car insurance company suspects that the younger the driver is, the more reckless a driver he/she is. They take a survey and group their respondents based on age. Of 217 respondents between the ages of 16-25 (Group 1), 183 claimed to wear a seat belt at all times. Of 398 respondents who were 26+ years old (Group 2), 322 claimed to wear a seat belt at all times. Find a 95% confidence interval for the difference in proportions. Can it be concluded that there is a difference in the proportion of drivers who wear a seat belt at all times based on age group? Enter the confidence interval - round to 3 decimal places.

Answer 1

soll In this question we want to test that u there any difference in the proportion of drivers who wear a seat belt at all times based on age group. Scanned with CamScanner

we will here - Test of significance for difference of properetionais I The procedure for this is as followsic Suppose we want to compare 2 distinct Ibobulations wirto the relevance of certain attribute. Al say among the members. det x 8 x be the no. of persons boss esing the given attribute in a random sample of sizes N. & Nz from the 's populations Then sample peroportions are Blæbe=X1B 2 = x2 M N2 Here Nuba Alyto thesis who ined With CamScanney!

: Test statistic is as follow Z statistic Pi-P2 S.E = pi - þz i pll-p] [14] LW N₂ * \z statisza < Z cucitias voted at significance level x. than we accept Null Hypothesis ie there is no difference between the probortions. W o thosuwise if IZStatistic > Raritical vost - w reject Null Hypothesis and We accept alternate hypothesis . there is a significant difference between the two po proportions. CScanned with CamScanner

sing above procedure Lact sample A represents 16-25 age group Sample B represents 26+ age group ist people wearing belt's peoprostion for Sample A is bi Sample B is' pz . bi = 183 & p2 = 322 217 398 Hypothesis ! Nule Hypothesis Ho: There is no difference between proporctions i. e. p = pz * cs$canned with CamScanner 1.1 .12

DATE: PAGE NO Alternate hypothesis - There is a significant difference O' between the two fleopobitious ie itp. 217 Sample A Sample B Sample size Nes_217_ Sample size N = 398 b = 183 p2 = 322 398 booled Sample picofortion ! by wing above formula i 217 Nt bzNz. NI+N2 6 = 183 x 317 + 322 x 398 217 398 217 +398 - کنگر IbE 018211 Standard euros I By thing above formula Ssanned with CamScanner NEN

DAJE: PAGE NO.: + 1 Casa Pli-p) I N Na 10.8 211) 10.1788) 213 39% = 110.4 0) (0.1788) 15. f. = 2.0.3239 f.=0.032 33 Test Statistic is calculated as: - 2 Statistic 3 þr- þz 183 217 -322 398 0.03233 = 0.03427 0:03233 Ferstin = 06009 at x = 0,0 5 for 2 tail test Z critical value is 1196 CS$canned with CamScanner

PAGE MO: - - - - t ² : we statistic) < z critical accept Neell Hypothesis . There is no difference between a beobortion te. The brobortion of drivers who wear a seat at at all times is not based on age group Confidence Internal 1 formula = 16-p2) Ź Z critical & S e . taon. von above formula By using critical value - 1.96 ÇE = 0.03232 0.0 34 27 bo-bz = 0.03427. a5%. Confidence interval = 0.03427 ± 1.96*0. 0323 • 9s. confidence interual = (0.0 2909, 0.09763 A Scanned with Camscanner Scanneke with Carnspanner