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Question – 1
(a)
The stem and leaf display for WPL and WOL is given below
WPL | Stem (Units = 10) | WOR |
0 | 5 6 7 9 9 | |
1 | 0 0 5 8 8 | |
2 | 1 6 8 | |
9 4 4 | 3 | 0 1 2 |
9 5 0 | 4 | 0 3 4 8 9 |
3 | 5 | 2 4 9 9 |
3 0 | 6 | 1 1 3 4 6 8 |
3 | 7 | 0 0 6 6 7 7 7 8 |
8 | 0 2 2 3 3 4 4 | |
2 | 9 | 1 |
9 8 7 7 6 3 3 2 2 1 1 0 | 10 | 6 7 9 |
6 6 5 4 4 3 2 | 11 | |
9 9 8 6 5 5 3 2 0 | 12 | 9 |
8 7 5 5 3 2 | 13 | |
9 1 | 14 | 1 |
3 3 | 15 | |
16 | ||
4 | 17 | |
2 | 18 |
The stem and leaf plot indicates that the open price of WOR is less when compared with WPL open price shares. In addition, the distribution of both WPL and WOR distribution has longer tail facing towards the left side of normal curve, which means that the distribution of WPL and WOR is skewed left
(b)
(c) Bar Chart
(d)
Proportion of Stock prices above $40 for WPL = 49/50 = 0.94
Proportion of Stock prices above $40 for WOR = 35/50 = 0.67
Question 2
(a)
The descriptive statistics is given below
Prices | |
Mean | 153.3245 |
Median | 141.63 |
First Quartile | 95.0925 |
Third Quartile | 216.73 |
(b)
The variation measures for Prices is given below
Prices | |
Standard Deviation | 75.66799 |
Range | 326.8 |
Coefficient of Variation | 49.35152 |
(c) The box whisker plot is given below
(d) Required student last four digit id no S0256033
Ewen, Dale, Joan S Gary, and James E Trefzger. Technical Calculus. Upper Saddle River, N.J.: Pearson/Prentice Hall, 2005. Print. ISBN – 13: 978-0-130-48818-3
Margaret L. Andersen, 2016. Sociology: The Essentials. 9 Edition. Cengage Learning. ISBN – 13: 978-1-305-50308-3
Michael Swan, 2005. Practical English Usage. 3 Edition. Oxford University Press. ISBN – 13: 978-0-194-42098-3
Louis P. Pojman, 2013. Philosophy: The Quest For Truth. 9 Edition. Oxford University Press. ISBN – 13: 978-0-199-96108-3
Question 3
(a) The total sources of agricultural water is 9779.7 (000 ML), out of which 1163.9 (000 ML) was used from on farm dams or tanks. Therefore,
P (water used from on-farm dams or tanks) = 1163.9/9779.7 = 0.119
(b) P (Groundwater and located in Qld) = 631.1/9779.7 = 0.065
(c) It is found that 1414.4 out of 6174.3 (000 ML) amount of water from MDB is taken from Rivers, creeks or lakes
P (water taken from Rivers, creeks or lakes for farm located in MDB) = 1414.4/6174.3 = 0.2291
(d) It is found that 957 out of 3425.8 (000 ML) amount of water from NSW is not taken from Rivers, creeks or lakes or Irrigation channels or pipelines
P (water not taken from Rivers, creeks or lakes or Irrigation channels or pipelines) =
957/3425.8 = 0.2794
Question 4
(i) Here, ? = 1.51 (average of overall rainfall)
P (x = 0) = e-1.51 = 0.221
(ii) Here, ? = 78.60/52 = 1.51 (average of weekly rainfall)
P (x = 0) = e-1.51 * (1.51)0 /0! = 0.221
P (x = 1) = e-1.51 * (1.51)1 /1!= 0.3334
P(X<2) = 0.221+0.3334 = 0.5543
P (X >=2) = 1 – P (X < 2) = 1 – 0.5543 = 0.4457
Therefore, the probability that there will be 2 or more days of rainfall in a week is 0.4457
(b)
The mean weekly total amount of rainfall is 10.58 and its standard deviation is 14.61
= P (-0.3136 < Z < 0.0972)
= P (-? < Z < 0.0972) – P (-? < Z < -0.3136)
= 0.5387 – 0.3769
= 0.1618
(ii)
------- (1)
On referring normal table, it is observed that
P (Z < 0.8416) = 0.80 ----------------------------- (2)
From (1) and (2), we have
=0.8416
A = 12.29
Therefore, we conclude that for the rainfall 12.29mm, only 20 % of the weeks have that amount of rainfall or higher
Question 5
(a) Normal Probability Plots
The points fall close to the trend line, indicating that the distribution of Temperature follows normal distribution, approximately
The points fall close to the trend line, indicating that the distribution of Relative Humidity follows normal distribution, approximately. Also, we see that there exist outliers in the dataset
The points fall close to the trend line, indicating that the distribution of Wind (km/hr) follows normal distribution, approximately
The points fall far away from the trend line, indicating that the distribution of Area burned do not follow normal distribution.
(b)
The formula used to calculate the 95% confidence interval for mean is given below
Here, the table value of z corresponding to 5% level of significance and is 1.96
Therefore, the margin of error, E is computed using this table value of t along with standard deviation and sample size.
The table given below shows the workings of 95% confidence interval for mean values
Temperature | Relative Humidity | Wind | Area Burned | |
Sample Standard Deviation | 6.603110477 | 17.43006 | 1.777181326 | 77.71624 |
Sample Mean | 47.40540541 | 21.54955 | 4.362162162 | 17.89532 |
Sample Size | 140 | 140 | 140 | 140 |
Level of Confidence | 95% | 95% | 95% | 95% |
Confidence Interval Workings | ||||
Se (Standard Error) | 0.558064691 | 1.473109 | 0.150199236 | 6.568221 |
Degrees of Freedom | 139 | 139 | 139 | 139 |
Z Value | 1.9600 | 1.9600 | 1.9600 | 1.9600 |
Interval Half Width | 1.0938 | 2.8873 | 0.2944 | 12.8737 |
Confidence Interval | ||||
Interval Lower Limit | 46.31 | 18.66 | 4.07 | 5.02 |
Interval Upper Limit | 48.50 | 24.44 | 4.66 | 30.77 |
The 95% confidence interval for the Temperature (0 Celsius) is (46.31, 48.50). This indicates that, when more number of samples are extracted from the same population, then there is a 95% chance (95 out of 100 times) the true mean Temperature (0 Celsius) will lie within this interval
The 95% confidence interval for the Relative Humidity (%) is (18.66, 24.44). This indicates that, when more number of samples are extracted from the same population, then there is a 95% chance (95 out of 100 times) the true mean Relative Humidity (%) will lie within this interval
The 95% confidence interval for the Wind (km/hr) is (4.07, 4.66). This indicates that, when more number of samples are extracted from the same population, then there is a 95% chance (95 out of 100 times) the true mean Wind (km/hr) will lie within this interval
The 95% confidence interval for the Area burned (ha) is (5.02, 30.77). This indicates that, when more number of samples are extracted from the same population, then there is a 95% chance (95 out of 100 times) the true mean Area burned (ha) will lie within this interval
(c) Hypothesis Testing
In order to determine whether more areas in the forest burn when the temperature is above 250 Celsius than when it is below 250 Celsius, we perform two mean z test. The null and alternate hypotheses are given below
Null Hypothesis: H0: µ1 = µ2
That is, the mean forest area burned when the temperature is above 250 Celsius is significantly not greater than the mean forest area burned when it is below 250 Celsius
Alternate Hypothesis: H0: µ1 > µ2
That is, the mean forest area burned when the temperature is above 250 Celsius is significantly greater than the mean forest area burned when it is below 250 Celsius
Level of Significance: The level of significance is set to be ? = 0.05
Test Statistic
The z test statistic is
Z=x1-x2s12n1+s22n2
The descriptive statistics for the two groups
Area burned (ha) > 25 degree | Area burned (ha) <=25 degree | |
Average | 29.0431 | 13.10816 |
Std dev | 117.2704 | 36.2119 |
Sample Size | 42 | 98 |
The table given below shows the workings of two mean z test
Data | |
Hypothesized Difference | 0 |
Level of Significance | 0.05 |
Area burned (ha) > 25 degree | |
Sample taken | 42 |
Mean for the sample | 29.0431 |
Standard deviation for the sample | 117.2704 |
Area burned (ha) <=25 degree | |
Sample taken | 98 |
Mean for the sample | 13.10816 |
Standard deviation for the sample | 36.2119 |
Testing Workings | |
Mean Difference | 15.93494 |
Standard Error | 18.4612 |
Z-Test Statistic | 0.8632 |
Upper-Tail Test | |
Upper Critical Value | 1.6449 |
p-Value | 0.1940 |
The value of z test statistic is 0.8632 and its corresponding p – value is 0.1940 > 0.05. This indicates that, the chance of rejecting the null hypothesis is violated. Therefore, we fail to conclude that more areas in the forest burn when the temperature is above 250 Celsius than when it is below 250 Celsius
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