A sample of308drive-thru visits at a single coffee company location and318drive-thru visits at a different location for the same company yielded data on service time. A summary of the results (in seconds) is shown below.

Chainn

x

s

Location 130858.0223.8Location 231867.521.2

(a)

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

2-sample t test for a difference in means

ANOVA

Paired t confidence interval for a mean difference

Paired t test for a mean difference

Chi-square test

2-sample t confidence interval for a difference in means

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 samples have no extreme outliers.

We must assume that the samples are random, but the sample size is large enough to use a t procedure without knowing whether the sample distribution is normal.

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, and we must assume that the population size is at least 10 times the sample size.

(b)

Construct a 95% confidence interval for the difference in average service time. Use location 2 - location 1, and round your answers to two decimal places. Degrees of freedom are 611.

,

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 one of the locations is in the interval.

We are 95% sure that the mean number of seconds longer we'll have to wait at one location over the other is in the interval.

We are 95% sure that the mean number of seconds longer we'll have to wait at location 1 over location 2 is in the interval.

95% of the time, the difference in lengths of time we'll have to wait between the locations is in the interval.

Lex could visit either location. Does the interval in part (b) contain the difference in their service times that they're likely to encounter? Explain your answer.

The confidence interval contains 95% of the individual differences in service times that they are likely to encounter.

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