Question

Using the accompanying data​ set, regress y=weight and x=capacity of battery. Complete parts a through c below.

Weight (g)=y Battery Capacity (mAh) =x

135,1592
132,904
136,1847
108,1402
153,1817
128,1493
138,1507
116,1020
130,1204
97,1201
150,1493
94,1118
112,1323
116,1491
147,1653
115,1505
89,888
130,1507
138,1194
107,1327
92,864
155,1828
131,2103
85,1054
136,1500
121,1129
77,646
132,1306
113,1291
160,1402
152,1208
136,1759
85,861
131,1866
184,1495
131,2096
171,1410
136,1538
127,1641
126,1232
143,1525
107,1040
137,1205
131,1309
121,1295
89,1019
164,1292
101,1505
158,1391
102,1313

a) Find a​ 95% confidence interval for the mean weight of cell phones with battery capacity1500 mAh. Interpret the interval with 95% confidence, the mean weight

of a phone with 1500 mAh of battery capacity falls between _______ grams and _______ grams.

​(Use ascending order. Round to the nearest integer as​ needed.)

b)Find a​ 95% prediction interval for the weight of a cell phone with a battery capacity of1500 mAh. Interpret.

c)Explain the differences between the purposes of the intervals in a and b.

Answer 1

(a) The 95% confidence interval is (125, 138).
The mean weight of a phone with 1500 mAh of battery capacity falls between 125 grams and 138 grams.

(b) 95% prediciton interval = (89.88, 172.91) = (90, 173) (if rounded to nearest integer).

(c) In case of a prediction interval, we are finding out an interval estimate inside which a future observation will lie, given the current observations. In case of a confidence interval, we are finding the interval estimate inside the mean value of the dependent variable will lie, which is unknown to us.