Question

In a metro region, 6 days in a typical month of 30 days have long commute times. (p=6/30). A study this past year showed only 3 days of long commute time (3/30). People suspect it is due to improvements in the public transportation system,. Based on minimal data in our sample, we cannot conclude that this is true. But we can test to see if the typical number of days in a month with long commute times is now less than 6.

a. test the claim using the p-value method at alpha level 0.02, stating the null and alternate hypotheses.

b, test the claim using the critical value method, including a picture sharing the critical region(s) and showing the test statistic.

Answer 1

Gires p= 6/30 = 0.2 x= 3 0=30, x=0.02 Hypothesis: W H,: p<0.2 Ho: p=0.2 This is left tailed test Test statistic: 2- p-p where P = 3 = 36.0.1 TP(1-P) V n 0.1-0.2 -1.37 10.2 (0.85 V 30 as fra snowd Finding p value in excel. use the command = NORMSDIST (-):37) P value = 0.0855 Decision Eute: Ho I p value <a reject Ho I p value xx Fail to reject Here P value (0.0855) > & co.org Hence are foul to reject to Conclusion: to support the a month with Jess than 6. Thea claim long jg not sufficient evidence that number of days in commute times is now

b) we have given d=0.02 - By using exced command = NORM SINN (0.02 -2:05 i we get Coitical value = -2.05 value, In diaq cam, shaded region shows Coitical zegion. Decosion cute; -2.051.37 o It Test statistics Circal ve thical reg reject Ho O Test statistic > Cortical region Fail to reject to Here Test stati. (-1.37) Critical value (-2.05) i ar fail to reject Ho Conclusion: There is not sufficient evidence to Support the claim that number of days with long commute timco is now Jess than 6.

Hope this will help you. Thank you :)