Question

Refer to the accompanying data set of mean​ drive-through service times at dinner in seconds at two fast food restaurants. Construct a 99​%

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            Y

79           103

118         129

119         152

150         113

262         175

176         131

125         109

149         127

167         131

210         128

329         133

308         137

178         225

110         217

155         291

146         128

98           90

237         140

244         244

189         143

149         148

202         205

170         145

117         141

60           140

205         147

182         161

119         130

139         172

168         132

186         236

199         232

232         249

193         237

354         229

302         168

212         85

192         107

182         52

192         169

105         80

152         140

175         140

156         94

176         129

160         144

168         128

122         184

138         148

312         125

Answer 1

99% confidence interval for restaurant x at dinner:

Sample size = n = 50

Sample mean = = 179.36

Standard deviation = s = 63.2161

We have to construct 99% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 50 - 1 = 49

Level of significance = 0.01

tc = 2.680    ( Using t table)

So confidence interval is ( 179.36 - 23.9591 , 179.36 + 23.9591) = > ( 155.4009 , 203.3191)

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99% confidence interval for restaurant x at dinner:

Sample size = n = 50

Sample mean = = 152.86

Standard deviation = s = 49.6572

We have to construct 99% confidence interval.

Formula is

Here E is a margin of error.

Degrees of freedom = n - 1 = 50 - 1 = 49

Level of significance = 0.01

tc = 2.680    ( Using t table)

So confidence interval is ( 152.86 - 18.8202 , 152.86 + 18.8202) = > ( 134.0398 , 171.6802)

Restaurant X has large confidence interval as compare to restaurant Y.