Question

Many people think it’s faster to order at the drive-thru than to order inside at fast-food restaurants.  To find out, two students randomly selected 10 times over a 2-week period to visit a local Dunkin’ Donuts restaurant.  At each of these times, one student ordered an iced coffee at the drive-thru and the other student ordered an iced coffee at the counter inside.  The table shows the times, in seconds, that it took for each student to receive their iced coffee after the order was placed.

1. After calculating the difference (inside - outside) data, find the mean difference. Label as dbar =
2. Find the standard deviation of the difference data. Label as SD(d) =
3. State the inference procedure.
4. Check the conditions.
5. What critical number will you use for a 95% confidence interval.
6. Construct a 95% confidence interval. Use the format dbar +/- MOE = (xxx, xxx)
7. Interpret the confidence interval.
8. How many trips to DD’s are needed to estimate the true mean difference to within 2 seconds of the true value? Use your standard deviation from #2.

The key is to obtain the correct mean and standard deviation. Double and Triple check your differences. USE TECHNOLOGY (EXCEL or your GRAPHING CALCULATOR) TO OBTAIN THE MEAN AND STANDARD DEVIATION.

Visit	Inside	Outside
1	62	55
2	63	50
3	327	321
4	105	111
5	135	124
6	57	54
7	98	90
8	75	69
9	205	200
10	100	103

Answer 1

visit	inside	outside	inside-outside
1	62	55	7
2	63	30	33
3	327	321	6
4	105	111	-6
5	135	124	11
6	57	54	3
7	98	90	8
8	75	69	6
9	205	200	5
10	100	103	-3
TOTAL	1227	1157	70

*Inside *outside

MEAN =122.7 MEAN =115.7

SD =84.2893 SD = 86.3997

1) MEAN differnce =7

SD of difference ,SD(d) =10.4563

2)

1.96

The critical value for a 95% confidence interval is 1.96, where (1-0.95)/2 = 0.025.

3) confidence interval

M = 7
Z = 1.96
sM = √(10.45632/10) = 3.31

μ = M ± Z(sM)
μ = 7 ± 1.96*3.31
μ = 7 ± 6.48

M = 7, 95% CI [0.52, 13.48].

You can be 95% confident that the population mean (μ) falls between 0.52 and 13.48.