Question

Use the data and develop 95% and 99% prediction intervals for the following A. the hours per week that an individual will spend in his vehicle B. the number of miles driven per week

Vehicle Driven	Type	Satisfaction with vehicle	Gender	Age	# of hours per week in vehicle	Miles driven per week	Number of Children	Average number of riders	Miles from work
Truck	Domestic	Yes	Male	31	10	450	0	1	30
Truck	Domestic	Yes	Male	29	5	370	1	1	22
Truck	Foreign	No	Male	26	12	580	0	1	15
Truck	Domestic	No	Male	18	6	300	0	1	20
SUV	Domestic	Yes	Male	49	21	1000	0	1	22
SUV	Foreign	Yes	Male	50	16	840	2	1	45
SUV	Domestic	Yes	Male	48	15	1400	3	4	25
SUV	Foreign	Yes	Male	45	5	300	2	2	20
SUV	Domestic	Yes	Male	45	15	850	0	1	25
SUV	Domestic	Yes	Male	44	10	700	2	1	40
SUV	Foreign	Yes	Male	41	5	350	1	1	20
SUV	Domestic	Yes	Male	41	30	1500	4	3	15
SUV	Foreign	No	Female	39	6	280	1	1	17
SUV	Foreign	Yes	Female	36	4	400	0	1	20
SUV	Foreign	Yes	Female	33	3	420	0	1	25
SUV	Domestic	Yes	Male	31	10	675	0	1	35
SUV	Domestic	No	Female	31	15	800	1	1	50
SUV	Domestic	No	Female	29	4	300	1	1	20
SUV	Domestic	Yes	Male	28	3	400	1	1	15
Mini Van	Domestic	Yes	Female	55	8	400	0	2	0
Mini Van	Domestic	No	Female	43	10	700	2	3	0
Mini Van	Domestic	Yes	Female	41	10	720	1	2	15
Mini Van	Foreign	Yes	Female	38	10	450	4	5	0
Mini Van	Foreign	Yes	Female	39	15	1000	1	2	0
Mini Van	Domestic	No	Male	35	5	350	2	2	0
Mini Van	Domestic	Yes	Female	33	10	800	2	3	0
Mini Van	Foreign	Yes	Female	32	2	200	4	5	5
Mini Van	Foreign	Yes	Female	28	8	350	3	4	0
Car	Domestic	Yes	Female	21	4	150	0	1	0
Car	Domestic	No	Female	62	5	175	0	2	0
Car	Domestic	Yes	Female	61	5	355	0	1	15
Car	Foreign	Yes	Male	60	5	150	0	1	10
Car	Domestic	No	Male	58	10	600	0	1	35
Car	Domestic	Yes	Female	51	11	600	0	1	40
Car	Domestic	Yes	Female	47	4	300	0	1	21
Car	Domestic	No	Male	46	4	275	0	1	18
Car	Domestic	No	Male	44	6	285	2	3	16
Car	Foreign	No	Female	42	5	400	2	3	22
Car	Foreign	Yes	Female	41	5	350	2	2	23
Car	Domestic	No	Female	41	10	600	1	2	34
Car	Domestic	Yes	Female	39	10	700	1	2	45
Car	Foreign	Yes	Female	34	10	600	1	2	16
Car	Foreign	Yes	Male	33	5	400	1	2	22
Car	Foreign	Yes	Male	30	5	350	1	2	18
Car	Domestic	Yes	Female	29	5	250	0	1	19
Car	Foreign	Yes	Female	27	6	355	0	2	23
Car	Foreign	Yes	Female	26	5	175	0	1	11
Car	Domestic	No	Female	24	5	300	0	1	4
Car	Domestic	Yes	Female	22	5	350	0	1	3
Car	Foreign	No	Female	19	5	500	0	2	4

Answer 1

Critical t-value for the 95% and 99% prediction interval are 2.0096 and 2.68 respectively.

Sample size =50

Obtained using Excel formula,=T.INV.2T(1-alpha, 49)

Now the sample mean and sample standard deviation are

	Sample Mean	Sample Standard deviation
hours per week individual will spend in the vehicle	8.16	5,1641
Number of miles driven per week	502.1	292.1648

Now Prediction interval formula for the unknown standard deviation of the population is

PI =x_bar

a.

95% Prediction Interval