Question

# Students compared drive-through times at a couple of fast food restaurants in their town to see...

Students compared drive-through times at a couple of fast food restaurants in their town to see if Wendy’s is faster than Hot n’ Now. They kept track of the time (in seconds) for people to go through the drive-through at Wendy'sand Hot 'n Now from the time of ordering until they exited the pick-up window during lunch time. The results are shown below.

 Sample size Sample mean Sample SD Wendy’s 27 93.7 46.7 Hot n’ Now 29 203 89.6

1.Write down the null and alternative hypothesis using symbols.

2.Calculate a theory-based t-statistic to test whether the average drive-through time for Wendy’s is faster than that of Hot n’ Now.

3.Based on the t-statistic, what can we conclude?

4.What is the type of error possible in this situation.

5.Construct a 95% CI for the difference in the average drive-through times between Wendy’s and Hot n’ Now. Interpret this interval.

Ans:

1)

2)

Test statistic:

t=(93.7-203)/sqrt((46.7^2/27)+(89.6^2/29))

t=-5.78

df=27-1=26

p-value=tdist(5.78,26,1)=0.0000

c)As,p-value<0.05,Reject the null hypothesis.

There is sufficient evidence to conclude that Wendy’s is faster than Hot n’ Now.

d)as we rejected null hypothesis,we could make type I error.

e)t*=tinv(0.05,26)=2.056

Margin of error=2.056*sqrt((46.7^2/27)+(89.6^2/29))=38.9

Point estimate=93.7-203=-109.3

lower limit=-109.3-38.9=-148.2

upper limit=-109.3+38.9=-70.4

We are 95% confident that average difference in drive through times lies between -148.2 and -70.4