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 e below.

Data_#   Temperature
1 54.1
2 52.8
3 48.5
4   44.3
5 43.3
6 52.6
7 46.8
8 44.6
9 43.5
10 50.9
11 47.3
12 48.8
13 59.9
14 56.7
15 53.3
16 45.1
17 46.5
18 59.3
19 42.3
20 42.5
21 43.1
22 50.7
23 43.7
24 49.7
25 45.3
26 55.9
27 57.6
28 46.1

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 . _____F. ​(Round to two decimal places as​ needed.)

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 . negative _____F. ​(Round to two decimal places as​ needed.)

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 . _____F. ​(Round to two decimal places as​ needed.)

d. Compare the sampling error for parts​ a, b, and c and explain the reason for the differences. Choose the correct answer below.

A. In​ general, increasing the sample size makes the sampling error increasingly negative.

B. In​ general, increasing the sample size has no effect on the sampling error.

C. In​ general, increasing the sample size makes the magnitude of the sampling error smaller. The sample obtained in part c does not follow this​ trend, however.

D. In​ general, increasing the sample size makes the magnitude of the sampling error larger. The sample obtained in part b does not follow this​ trend, however

What problems might be encountered with the sample obtained in part​ c?

A. The larger sample obtained in part c might lead to a larger diversion from the data.

B. The presence of periodicity in the data might impact the sample obtained in part c.

C. The lack of periodicity in the data might impact the sample obtained in part c.

Answer 1

To find the sampling error we need to find the population mean. Following table shows the calculations:

Data_#	Temperature
1	54.1
2	52.8
3	48.5
4	44.3
5	43.3
6	52.6
7	46.8
8	44.6
9	43.5
10	50.9
11	47.3
12	48.8
13	59.9
14	56.7
15	53.3
16	45.1
17	46.5
18	59.3
19	42.3
20	42.5
21	43.1
22	50.7
23	43.7
24	49.7
25	45.3
26	55.9
27	57.6
28	46.1
Total	1375.2

The population mean is:

Following is the screen shot of the random number table:

Starting from first row and first column the first selected number between 01 and 28 is 11.

(a)

Since we need to selected 2 data values out of 28 data values so we need to select every 28/2 = 14th data value.

First data value selected is 11th data value and second is 11+14 = 25th data value. So selected sample is:

Data	Temperature
11	47.3
25	45.3
Total	92.6

The sample mean is

The sampling error is

(b)

Since we need to selected 4 data values out of 28 data values so we need to select every 28/4 = 7th data value.

First data value selected is 11th data value, second is 11+7 = 18th data value, third is 18+7 = 25th data value and fourth data value 25+7 = 32 that is 4th data value . So selected sample is:

Data	Temperature
4	44.3
11	47.3
18	59.3
25	45.3
Total	196.2

The sample mean is

The sampling error is

(c)

Since we need to selected 7 data values out of 28 data values so we need to select every 28/7 = 4th data value.

First data value selected is 11th data value, second is 11+4 = 15th data value, third is 15+4 = 19th data value and so on. So selected sample is:

Data	Temperature
3	48.5
7	46.8
11	47.3
15	53.3
19	42.3
23	43.7
27	57.6
Total	339.5

The sample mean is

The sampling error is

Correct options:

C. In​ general, increasing the sample size makes the magnitude of the sampling error smaller. The sample obtained in part c does not follow this​ trend, however.

B. The presence of periodicity in the data might impact the sample obtained in part c.