Sampling Distribution and Hypothesis Testing

2.3-Sampling Distribution and Hypothesis Testing
PART 1
Question 1: Method to calculate the sampling distributions
The first step was randomly selecting 100 values and subjecting them to 100, 200, and 1000
iterations. In order to do this successful an excel function was used to select random data values
for the 1999 dataset (i.e.
=INDEX($A$2:$A$1737,RANDBETWEEN(1,COUNTA($A$2:$A$1737)),1). This function
was used to populate a table of value with sample size (100) on the left side and iterations
(100,200, or 1000) on the top. The values where then copied and pasted back into the same
position (void of the function) to prevent the continuous refreshing of values usually caused by
the “RandBetween” function.
In order to determine the sampling distribution a histogram plot approach was employed; where
the mean water discharge values are put into equal classes ranging between 1 and 3. The
frequencies are plotted against the classes (bins) to get the sampling distribution. In addition, the
descriptive statistics will be computed to be used in further interpretation of the results. For
example, the skewness and kurtosis will be used as a foundation for the test of normality as well
as the size difference between mean and median.
Question 2: Calculation of the sampling distributions i.e. Plots and Statistics
1 1.2 1.4 1.6 1.8 2 2.1 2.2 2.4 2.6 2.8
0
5
10
15
20
25
30
35
40
100 Sample Distribution
Mean
Frequency
100 sample
Mean 1.8557964
Standard Error 0.020604847

Median 1.835425
Mode #N/A
Standard
Deviation
0.206048468
Sample
Variance
0.042455971
Kurtosis 1.36986228
Skewness 0.843467534
Range 1.18166
Minimum 1.47124
Maximum 2.6529
Sum 185.57964
Count 100
1 1.2 1.4 1.6 1.8 2 2.1 2.2 2.4 2.6 2.8 3
0
10
20
30
40
50
60
70
80
200 Sample Distribution
Mean
Frequency
200 Sample
Mean 1.806265
Standard Error 0.014062
Median 1.804865
Mode #N/A
Standard
Deviation
0.198874
Sample
Variance
0.039551
Kurtosis 2.316882
Skewness 0.869112

Range 1.36011
Minimum 1.35779
Maximum 2.7179
Sum 361.253
Count 200
1 1.2 1.4 1.6 1.8 2 2.1 2.2 2.4 2.6 2.8 3
0
50
100
150
200
250
300
350
400
1000 Sample Distribution
Mean
Frequency
1000 Sample
Mean 1.842174
Standard Error 0.00645
Median 1.825495
Mode #N/A
Standard
Deviation
0.203981
Sample
Variance
0.041608
Kurtosis 0.272112
Skewness 0.452909
Range 1.37319
Minimum 1.35053
Maximum 2.72372
Sum 1842.174
Count 1000
Question 3: Conclusion (Interpreting the results)