Calculation: To calculate the standard deviation for four regions with reference to Exercise 7.79 and Exercise 7.80 (page 459), on excel following steps were followed:

Step 1: Open the data set for exercise 7.79. The partial screenshot is shown below:

Step 2: Write the standard deviation formula =STDEV.S(B2:B31) under the formula tab and then select the data for north as:

Step 3: Write the standard deviation formula =STDEV.S(B32:B61) under the formula tab and then select the data for south as:

Step 4: Open the data set for exercise 7.80. The partial screenshot is shown below:

Step 5: Go to the Write the standard deviation formula =STDEV.S(B2:B31) under the formula tab and then select the data for east as:

Step 6: Write the standard deviation formula =STDEV.S(B2:B31) under the formula tab and then select the data for west as:

To see the impact of standard deviation on power statistic, consider arbitrary choose some different σ and calculate the power for each σ value. The power is represented as P(z>t*−δ), where δ is the noncentrality factor which depends on σ.

For σ1=7.4, the noncentrality parameter can be obtained as:

The noncentrality parameter(δ)=μ1−μ2σ1(2n)=57.4(245)=3.21

The power can be calculated as:

Power=P(z>t*−δ)=P(z>1.99−3.21)=P(z>−1.22)=0.8888

For σ2=7.7, the noncentrality parameter can be obtained as:

The noncentrality parameter(δ)=μ1−μ2σ2(2n)=57.7(245)=3.08

The power can be calculated as:

Power=P(z>t*−δ)=P(z>1.99−3.08)=P(z>−1.09)=0.8621

For σ3=8, the noncentrality parameter can be obtained as:

The noncentrality parameter(δ)=μ1−μ2σ2(2n)=58(245)=2.964

The power can be calculated as:

Power=P(z>t*−δ)=P(z>1.99−2.964)=P(z>−0.974)=0.8350

Noise is the unexpected variation in experiments. To consider their effect, it is recommended to choose larger value of σ than their experimental value.