Level of confidence and width of the confidence interval

Question

Discussion:

Q1) Calculate a point estimate and a 95% confidence interval of the mean. Assuming your data set is normally distributed, determine an appropriate sample size if the maximum allowable error is three units for the below data set. Use a 90% confidence level to determine the sample size.

Q2) Interpret the relationship between the level of confidence and the width of the confidence interval.

Price	Bedrooms	Size	Pool	Distance	Twnship	Garage	Baths
263.1	4	2300	1	17	5	1	2
182.4	4	2100	0	19	4	0	2
242.1	3	2300	0	12	3	0	2
213.6	2	2200	0	16	2	0	2.5
139.9	2	2100	0	28	1	0	1.5
245.4	2	2100	1	12	1	1	2
327.2	6	2500	0	15	3	1	2
271.8	2	2100	0	9	2	1	2.5
221.1	3	2300	1	18	1	0	1.5
266.6	4	2400	0	13	4	1	2
292.4	4	2100	0	14	3	1	2
209	2	1700	0	8	4	1	1.5
270.8	6	2500	0	7	4	1	2
246.1	4	2100	0	18	3	1	2
194.4	2	2300	0	11	3	0	2
281.3	3	2100	0	16	2	1	2
172.7	4	2200	1	16	3	0	2
207.5	5	2300	1	21	4	0	2.5
198.9	3	2200	1	10	4	1	2
209.3	6	1900	1	15	4	1	2
252.3	4	2600	0	8	4	1	2
192.9	4	1900	1	14	2	1	2.5
209.3	5	2100	0	20	5	0	1.5
345.3	8	2600	0	9	4	1	2
326.3	6	2100	0	11	5	1	3
173.1	2	2200	1	21	5	1	1.5
187	2	1900	0	26	4	0	2
257.2	2	2100	0	9	4	1	2
233	3	2200	0	14	3	1	1.5
180.4	2	2000	0	11	5	0	2
234	2	1700	0	19	3	1	2
207.1	2	2000	0	11	5	1	2
247.7	5	2400	0	16	2	1	2
166.2	3	2000	1	16	2	1	2
177.1	2	1900	0	10	5	1	2
182.7	4	2000	1	14	4	0	2.5
216	4	2300	0	19	2	0	2
312.1	6	2600	0	7	5	1	2.5
199.8	3	2100	0	19	3	1	2
273.2	5	2200	0	16	2	1	3
206	3	2100	1	9	3	0	1.5
232.2	3	1900	1	16	1	1	1.5
198.3	4	2100	1	19	1	1	1.5
205.1	3	2000	1	20	4	0	2
175.6	4	2300	1	24	4	1	2
307.8	3	2400	1	21	2	1	3
269.2	5	2200	0	8	5	1	3
224.8	3	2200	0	17	1	1	2.5
171.6	3	2000	1	16	4	0	2
216.8	3	2200	0	15	1	1	2
192.6	6	2200	1	14	1	0	2
236.4	5	2200	0	20	3	1	2
172.4	3	2200	0	23	3	0	2
251.4	3	1900	0	12	2	1	2
246	6	2300	0	7	3	1	3
147.4	6	1700	1	12	1	0	2
176	4	2200	0	15	1	1	2
228.4	3	2300	0	17	5	1	1.5
166.5	3	1600	1	19	3	0	2.5
189.4	4	2200	0	24	1	1	2
312.1	7	2400	0	13	3	1	3
289.8	6	2000	0	21	3	1	3
269.9	5	2200	1	11	4	1	2.5
154.3	2	2000	0	13	2	0	2
222.1	2	2100	0	9	5	1	2
209.7	5	2200	1	13	2	1	2
190.9	3	2200	1	18	3	1	2
254.3	4	2500	1	15	3	1	2
207.5	3	2100	1	10	2	0	2
209.7	4	2200	1	19	2	1	2
294	2	2100	0	13	2	1	2.5
176.3	2	2000	1	17	3	0	2
294.3	7	2400	0	8	4	1	2
224	3	1900	1	6	1	1	2
125	2	1900	0	18	4	0	1.5
236.8	4	2600	1	17	5	1	2
164.1	4	2300	0	19	4	0	2
217.8	3	2500	0	12	3	0	2
192.2	2	2400	0	16	2	0	2.5
125.9	2	2400	0	28	1	0	1.5
220.9	2	2300	1	12	1	1	2
294.5	6	2700	0	15	3	1	2
244.6	2	2300	0	9	2	1	2.5
199	3	2500	1	18	1	0	1.5
240	4	2600	0	13	4	1	2
263.2	4	2300	0	14	3	1	2
188.1	2	1900	0	8	4	1	1.5
243.7	6	2700	0	7	4	1	2
221.5	4	2300	0	18	3	1	2
175	2	2500	0	11	3	0	2
253.2	3	2300	0	16	2	1	2
155.4	4	2400	1	16	3	0	2
186.7	5	2500	1	21	4	0	2.5
179	3	2400	1	10	4	1	2
188.3	6	2100	1	15	4	1	2
227.1	4	2900	0	8	4	1	2
173.6	4	2100	1	14	2	1	2.5
188.3	5	2300	0	20	5	0	1.5
310.8	8	2900	0	9	4	1	2
293.7	6	2400	0	11	5	1	3
179	3	2400	0	8	4	1	2
188.3	6	2100	1	14	2	1	2.5
227.1	4	2900	0	20	5	0	1.5
173.6	4	2100	0	9	4	1	2
188.3	5	2300	0	11	5	1	3
221.1029	3.8	2223.81	0.361905	14.62857	3.104762	0.67619	2.080952	Arithmetic Mean
213.6	4	2200	0	15	3	1	2	Median
188.3	4	2100	0	16	4	1	2	Mode
227.824	5	304.5833	0.5	15.85	3	0.5	2.25	Weighted Mean