Question

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 95​% confidence interval estimate of the mean​ drive-through service time for Restaurant X at​ dinner; then do the same for Restaurant Y. Compare the results.

Restaurant X	Restaurant Y
85	102
125	130
115	149
141	111
265	174
185	138
126	113
151	123
165	131
212	127
337	137
311	139
176	226
117	218
161	298
149	128
95	93
234	135
238	241
189	147
155	145
203	204
170	150
121	143
63	136
199	145
182	162
117	135
138	166
172	134
185	238
200	237
236	255
196	237
352	233
307	171
214	90
201	110
178	50
192	176
110	81
146	143
181	148
153	96
176	131
157	148
170	135
119	180
137	150
308	125

Answer 1

	Restaurant X	Restaurant Y
count	50	50
mean	180.30	154.28
sample standard deviation	63.24	50.08
sample variance	3,999.93	2,508.37
confidence interval 95.% lower	162.77	140.40
confidence interval 95.% upper	197.83	168.16
margin of error	17.53	13.88
z	1.96	1.96
confidence interval 95.% lower	162.33	140.05
confidence interval 95.% upper	198.27	168.51
margin of error	17.97	14.23
t(df = 49)	2.01	2.01

Restaurant X confidence interval

162.8<u<197.8

Restaurant Y confidence interval

140.4<u<168.2

The confidence of two restaurants overlap so the results are not significant.