Question

One of the town council members believes that the two fire stations have different mean response times. Do you agree? Why? Use a significance level of 0.05 and the p-value to make your decision. Again, the data for both stations has been re-copied for convenience. Northern: 3,3,3,3,4,4,4,4,4,5,5,5,5,5,5, 6, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 12 Southern: 4,4,4,4,5,5,5,5,5,5,5, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 12, 12, 12, 12, 13 Answer in the blanks to show the work associated with exploring this claim. To explore the suspicion above, conduct a significance test using the hypotheses: Ho : Hi = 42 Họ : H1 + H2 Blank #1: Report the test statistic to two decimal places Blank #2: Report the p-value to four decimal places Blank #3: Give the test decision: (reject or do not reject) Ho

Answer 1

ANSWERS Here the hypotheses to be tested are Ho: Mr Hz Us Hq : Hi & M2 can ta 0+02-2 use independent sample t-test to test the above hypotheses Test statistic t- ša - X nis²+0252² क to the 561= mean of first group (Northern) 5,= Mean of second group (Southern 0,= Size of first group n2 = Size of Second group 5,²= variance of first group s² = variance of second group Forom the gives values of northero and Southern we get the following results

5c1= 6.4 52= 7.5 ni 30 0230 S,? 6.8 S2 7.98 Hence the value of test statistic is t=-1:57 From tables Of t-distribution the two-tailed critical value for 0.05 significance level is 2.0017 P-value O: 1225 Here P-value is greater than 0.057 Hence we accept (do not reject) Ho Evidence does not favor that there is a difference in mean response times of the two fire stations

If we use significance level 0.01, the critical value from t-clistribution table is 2-6633 If we use significance level 0.10 the critical value from t-distribution table is 1.6716 In both of these cases we do not reject Ho. (Because test statisticſ Coitical value we will reach in the same Hence Condusion Black #1 -1:57 Blank #2 0.12251 Blank #3 do not reject Ho does not favor Blank #4 Blank # 5 Yes