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.

Service Times (seconds)

Restaurant X Restaurant Y

82                   102

121                 130

117                 152

144                 111

269                 173

184                 135

127                 107

154                 120

161                 128

214                 126

337                 132

305                 132

177                 230

116                 212

153                 292

152                 128

93                   96

235                 135

237                 243

190                 142

156                 147

204                 203

166                 152

121                 142

68                   134

206                 146

178                 159

121                 136

142                 166

177                 138

193                 239

194                 235

231                 252

191                 239

349                 236

302                 165

214                 82

193                 106

182                 56

191                 173

103                 80

144                 149

179                 139

160                 97

174                 130

158                 146

168                 129

123                 183

138                 154

309                 130

Answer 1

Used R, on R.H.S is the R output and on L.H.S. is R code.

The 95 % Confidence interval for X is (162.7074 ,197.4126)

The  95 % Confidence interval for Y is ( 139.5117 ,167.2483) .

Service time for restaurant X is greater than restaurant Y. As lower limit and upper limit for X is greater than restaurant Y.