Question

A magazine assessed 1855 drive-thru visits at quick-service restaurants. One benchmark that was measured was the service time. A summary of the results (in seconds) for two of the chains is shown below.

Chain	n	x	s
Taco Bell	308	158.03	33.7
McDonald's	317	189.49	41.3

(a)

To estimate the difference in service times, what procedure is appropriate?

Paired t confidence interval for a mean difference2-sample t test for a difference in means    Paired t test for a mean difference2-sample z confidence interval for a difference in proportions2-sample t confidence interval for a difference in means2-sample z test for a difference in proportions

Which of the statements below reflects the extent to which we know conditions are met?

We must assume that the samples are random, and we must assume that the population size is at least 10 times the sample size.We must assume that the samples are random, and we must assume that the samples have no extreme outliers.    We are given that the samples are random, that the population size is at least 10 times the sample size, and that the samples are normally distributed.We must assume that the samples are random, but the sample size is large enough to use a t or z procedure without knowing whether the sample distribution is normal.

(b)

Construct a 95% confidence interval for the difference in average service time. Use McDonald's - Taco Bell, and round your answers to two decimal places.

  ,

sec

(c)

Which of the following sentences is the best interpretation of the interval in (b)?

We are 95% sure that the mean length of time we'll have to wait at Taco Time or McDonald's is in the interval.We are 95% sure that the mean number of minutes longer we'll have to wait at one restaurant over the other is in the interval.    We are 95% sure that the mean number of minutes longer we'll have to wait at McDonald's over Taco Time is in the interval.95% of the time, the length of time we'll have to wait at Taco Time or McDonald's is in the interval.

Lex plans to go to Taco Bell and Sam to McDonald's. Does the interval in part (b) contain the difference in their service times that they're likely to encounter? Explain your answer.

Yes, the confidence interval contains the difference in their service times that they are likely to encounter.No, the confidence interval is for the mean difference in time, not the difference for individuals.    

Answer 1

a)

2-sample t confidence interval for a difference in means

We are given that the samples are random, that the population size is at least 10 times the sample size, and that the samples are normally distributed.

b)

α=	0.05
df	605.0344

CI	Unequal variance
tc	1.963892817	T.INV.2T(alpha,df)
Upper	37.37390404	(X1 bar-X2 bar )+tc*SQRT(S1^2/n1 + S2^2/n2)
Lower	25.54609596	(X1 bar-X2 bar )-tc*SQRT(S1^2/n1 + S2^2/n2)

CI = (25.55, 37.37)

c)

We are 95% confident that population mean difference is lies between the interval

No, the confidence interval is for the mean difference in time, not the difference for individuals.