Students compared drivethrough 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 drivethrough at Wendy'sand Hot 'n Now from the time of ordering until they exited the pickup 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 theorybased tstatistic to test whether the average drivethrough time for Wendy’s is faster than that of Hot n’ Now.
3.Based on the tstatistic, 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 drivethrough times between Wendy’s and Hot n’ Now. Interpret this interval.
Ans:
1)
2)
Test statistic:
t=(93.7203)/sqrt((46.7^2/27)+(89.6^2/29))
t=5.78
df=271=26
pvalue=tdist(5.78,26,1)=0.0000
c)As,pvalue<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=93.7203=109.3
lower limit=109.338.9=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
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