Question

The air temperature is measured every 6 hours for one week. The temperatures are given in the data table. Use the data to complete parts a through c below.

Data#   Temperature
1   42.3
2   59.8
3   41.3
4   48.6
5   42.5
6   56.8
7   49.9
8   47.7
9   53.5
10   58.7
11   53.4
12   42.8
13   58.3
14   58.4
15   59.6
16   40.4
17   57.2
18   56.9
19   52.9
20   40.4
21   41.4
22   51.1
23   51.4
24   48.3
25   43.3
26   59.8
27   51.4
28   47.2

a. Draw a systematic sample consisting of 2​ temperatures, and then calculate the sampling error for the sample.

The sampling error for the sample is_____degrees°F.

b. Draw a systematic sample consisting of 4​ temperatures, and then calculate the sampling error for the sample.

The sampling error for the sample is____degrees°F.

c. Draw a systematic sample consisting of 7​ temperatures, and then calculate the sampling error for the sample.

The sampling error for the sample is____degrees°F.

Answer 1

in the systematic sampling, it selects from some starting point and then selects every kth element in population.

here for 2 samples, select data 1 and data 15

for sample 4 , select data 1 ,every 7th element(28/4=7)

for sample 7,select data 1,and then every 4th element(28/7=4)

Sr. no	X	systematic sample consisting of 2 temperatures	systematic sample consisting of 4 temperatures	systematic sample consisting of 7 temperatures
1	42.3	42.3	42.3	42.3
2	59.8
3	41.3
4	48.6
5	42.5			42.5
6	56.8
7	49.9
8	47.7		47.7
9	53.5			53.5
10	58.7
11	53.4
12	42.8
13	58.3			58.3
14	58.4
15	59.6	59.6	59.6
16	40.4
17	57.2			57.2
18	56.9
19	52.9
20	40.4
21	41.4			41.4
22	51.1		51.1
23	51.4
24	48.3
25	43.3			43.3
26	59.8
27	51.4
28	47.2
total	1415.3	101.9	200.7	338.5

population mean=ΣX/n =1415.3/28 = 50.5464

a)a. Draw a systematic sample consisting of 2​ temperatures, and then calculate the sampling error for the sample.

sample mean for 2 samples = 101.9/2=50.95

sampling error = population mean-sample mean = 50.5464 - 50.95 = -0.4036

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b)

sample mean for 4 samples = 200.7/4=50.175

sampling error = 50.55 - 50.175 = 0.37

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c)

sample mean for 7 samples=338.5/7=48.3571

sampling error = 50.55-48.3571 = 2.189