Question

A HMO researcher wants to test the claim that the waiting time for a doctor's appointment is less than two weeks. To this end, he modeled 25 HMO members who booked an appointment with a family doctor in the past month and found that the average waiting time for an appointment with a family doctor was 6 days, and the standard deviation is 8.11 days. Assume that the waiting time is distributed normally. *Is the researcher's claim correct at a significance level of 5%? * For each level of significance less than 5%, will the same conclusion be obtained without further calculation? * What is the confidence interval for waiting time for a column at a confidence level of 99%? --

Answer 1

solution or From the given information, dample mean , X = 6 days Jample stoi deviation S= 8.11 days Qample size D=25 Hereg Hypothized mean = 2 Weeks = 14 days op hull and Alternative Hypotheses Hoi ll s14 Ha! l 714 Thia corresponds to a sight-tailed test for which a test-torone mean will be eised & Pejection Region & Here signiticance level Q=0.05 and the chical value tc-1711 .:: Pejection region R'{t: t > 1.71} * Test statistic :- The t-statistic ia computed as t = X-llo = 6-14 -4,932 Slo 8:11|yas .. t -4.952 * Decision about the null hypothesis since it is observed t = -14.932 s tc 51.7, it is concluded that the pull hippotheaia is not rejected. thal, CScanned With CamScanner

of conclusion is It is concluded that null bypo- theaia io Dot rejected. je dejectegli accepleol Therefore there ja enough evidence to Claim that they Waiting time for doctors appointment is less than 14 days ie. 2 reeks. at level of s os algnificance For algniticance level q=0.01. the rejection region is, Ri tit > 2.492. Tie Here conical value tc = 2.492 E t = -4.932 3 tc = 2,492 the Dus hypothesis is not rejected.. And the 99% contidence interval is, e 8.17 1.465 < el < 10.537 6 for signiticance level a=0.02 the critical value is tc=2.172 & the rejection region is, Ri{ti I 7 2.1723 t = -4.932 Stc = 21172 :'. The null hypothesis is not oejectedl. For gigniticance level 220103 the critical value is tc=11974 "? t = -4.95 25 tc=11974. .: the Dull bypothesis is not rejected. |CScanned with CamScanner

classmate Date Page @ For significance level a=0.04 the critical value is tc=11828 ita-4.932 Ste = 1.828 - The null hypothesis is not rejected. & Conduzione For all the level of significance q=0.0110.03 0.03 0.04 the null ny po- theaja oot rejected.ie accepted. Thani's there a enough evidence to claim that the waiting time for doctor's appoinment ho less than ke days i-e. 2 weeks. of The ggol. contidence interval for the waiting time too is 1.463<< 10.537 CScanned with CamScanner