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. _# Temperature 1 45.4 2 56.7 3 49.2 4 45.2 5 43.2 6 53.6 7 48.6 8 43.7 9 54.2 10 53.8 11 50.2 12 44.9 13 53.4 14 57.5 15 56.8 16 49.7 17 41.2 18 58.7 19 55.2 20 42.2 21 49.3 22 57.1 23 58.8 24 41.5 25 40.4 26 51.4 27 55.8 28 45.4

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

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 ___ 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. In general, increasing the sample size has no effect on the sampling error. 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. 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. In general, increasing the sample size makes the sampling error increasingly negative.

e. What problems might be encountered with the sample obtained in part c? The presence of periodicity in the data might impact the sample obtained in part c. The lack of periodicity in the data might impact the sample obtained in part c. The larger sample obtained in part c might lead to a larger diversion from the da

Answer 1

We have 28 temperature readings.

Temprature: 1 45.4 2 56.7 3 49.2 4 45.2 5 43.2 6 53.6 7 48.6 8 43.7 9 54.2 10 53.8 11 50.2 12 44.9 13 53.4 14 57.5 15 56.8 16 49.7 17 41.2 18 58.7 19 55.2 20 42.2 21 49.3 22 57.1 23 58.8 24 41.5 25 40.4 26 51.4 27 55.8 28 45.4

Mean temprature =50.1 F

Standard deviation=5.9 F

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

For systematic sampling we select 1st and k= N/n =28/2=14th term

45.4 and 57.5

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 ___ F. (Round to two decimal places as needed.)

For systematic sampling we select 1st and k= N/n =28/4=7th,14th,21st terms

45.4,48.6,57.5 and 49.3

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.)

For systematic sampling we select 1st and k= N/n =28/7=4th, 8th,...28th

45.4,43.2,54.2,53.4,41.2,49.3,40.4

In general, increasing the sample size makes the magnitude of the sampling error smaller.