Question

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 90​% 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. LOADING... Click the icon to view the data on​ drive-through service times. Construct a 90​% confidence interval of the mean​ drive-through service times at dinner for Restaurant X. Construct a 90​% confidence interval of the mean​ drive-through service times at dinner for Restaurant Y.

Restaurant X   Restaurant Y
79   105
116   124
118   156
142   114
266   173
180   139
124   109
151   126
162   132
215   131
329   137
312   136
173   232
109   212
156   297
144   125
101   96
234   141
237   239
185   146
151   146
201   203
166   153
118   146
67   138
202   151
178   153
118   138
144   169
172   139
188   239
201   231
231   254
192   234
348   236
308   168
208   82
192   104
184   50
189   175
107   75
147   150
172   147
156   102
173   122
155   147
165   127
121   188
136   147
310   129

Answer 1

For restaurant X

90% confidence interval for the mean​ drive-through service times at dinner at restaurant X is obtained using the formula,

Given:

Sample mean	178.66
Sample SD	62.98286
Count	50
t	1.676551

The t-critical value is obtained from t critical value table for 90% confidence interval and degree of freedom = n - 1 = 50 - 1 = 49.

For restaurant Y

90% confidence interval for the mean​ drive-through service times at dinner at restaurant Y is obtained using the formula,

Given:

Sample mean	154.26
Sample SD	50.11041
Count	50
t	1.676551

Comparison of results

Since confidence interval for mean​ drive-through service times at dinner at restaurant X and Y overlap, the null hypothesis is not rejected. Hence there is no significant difference between the two restaurant.