2. A comparison is made between two bus lines to determine if arrival times of t

Question

2. A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of x =53 minutes with S1-19 minutes. For 60 randomly selected bus runs, bus line B was observed to be off schedule an average of ,-62 minutes with s2 15 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% significance level 2 Climd Grechman veight aain. IIse the sample data in the table helow with a 005 sioniffcance level to

Explanation / Answer

Here we have to compare if the mean times of the two bus lines are the same. So let u1 be the mean of bus line 1at the popluation level and u2 be the mean of bus line 2 at the population level. Thus our null hypothesis is that the means are equal i.e. Ho: u1=u2 and our alternate hypothesisis that Ha: u1 ! = u2

Now we calculate a t test statistic such that t = (u1-u2) / SQRT(s1^2/n1 + s2^2/n2) where s1 is the std. dev of bus line 1 for 51 obs and s2 is the std dev of line2 for 60 obs

this t = (53-62)/SQRT(19^2/51 + 15^2/60) = -2.735

Again since this is a two tail test the p value will be the area under the std. normal curve to the right of t= 2.735 plus the area to the left of t = -2.735 which would be between 0.001 and 0.01

Since the highest estimate of 0.01 < 0.05 (5% sig level ) we can be 95% confident that we can reject the null hypothesis of u1 = u2.

Hence there is sufficient evidene to say that there is a significant difference in avg off schdule times for the two lines

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.