y is conducted to estimate the average A parking stud parkin

y is conducted to estimate the average A parking stud parking space occupancy time period in a parking lot in a hypothetical city. The observed occupancy period in minutes for all parking spots in the lot (i.e., the population observations) are given in the table below (80 parking slot). 77 98 66 98 67 81 65 44 48 69 78 59 A) Compute the average and standard deviation of parking period for all parking spots in the lot. Hint: They represent the mean and the standard deviation of the entire population]. B) Pick 30 samples from these observations (the population) such that each sample includes three observations. c Pick 30 random samples from these observations (the population) such that each sample includes fifteen observations. D) Compare the sampling methodologies used in (B) and (C) by computing the following for both cases: Frequency distribution of the sampled parking period The mean of the sample distribution The variance of the sample distribution E) Which of the two sampling methodologies better population\'s mean and standard estimate the deviation?

Solution

a) The average parking period can be calculated as the parking load per hour to the parking volume.

the parking load for the above is addition of all the parking durations i.e (46+120+33+94+101........+25+24)/60=4776/60

=79.6 vehiles per hours

parking volume=80

average parking period=79.6/80=0.995 or 59.7 minutes

standard daviation of parking period of all 80 spaces can be calculated as (59.7-x) minutes where x stands for an observation. for eg. standard daviation of first space=(59.7-46) = 13.7 minutes

b)

30 87   59.7 -27.3

like this the samples having equal positive and negative standard deviations can be grouped to get the new mean.

s.no	parking period	mean parking period	standard daviation
1	46	59.7	13.7
2	33	59.7	26.7
3	101	59.7	-41.3
4	35	59.7	24.7
5	23	59.7	36.7
6	15	59.7	44.7
7	56	59.7	3.7
8	55	59.7	4.7
9	49	59.7	10.7
10	48	59.7	11.7
11	112	59.7	-52.3
12	69	59.7	-9.3
13	65	59.7	-5.3
14	35	59.7	24.7
15	44	59.7	15.7
16	115	59.7	-55.3
17	125	59.7	-65.3
18	19	59.7	40.7
19	47	59.7	12.7
20	75	59.7	-15.3
21	65	59.7	-5.3
22	67	59.7	-7.3
23	78	59.7	-18.3
24	85	59.7	-25.3
25	24	59.7	35.7
26	98	59.7	-38.3
27	16	59.7	43.7
28	96	59.7	-36.3
29	60	59.7	-0.3