Question 2. Note that the following problem is similar to scenario E in the previous question. However, it is not exactly the same. Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency. For one vehicle equipped in this way, the number of ‘liters per 100 kilometers’ driven were recorded each time the gas tank was filled, and the computer was then reset. Below are the ‘liters per 100 kilometers’ driven for a random sample of 20 of these records. 5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3, 4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4. Calculate a 95% confidence interval for the average liters per 100 kilometres for this vehicle. Use RStudio or R on Jupyter in order to solve this problem. Provide all your work with your solutions. Is the CI you obtained valid? In order to answer this question, • List all assumptions required. • For each assumption, indicate whether it holds and why it does or does not. • When appropriate, provide graphical displays in order to assess a particular assumption. • Explain how based on such graphs, you decided whether the corresponding assumption seems to hold or not.
R code:
X=c(5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3,
4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4)
t.test(X,conf.level = 0.95)
Output:
One Sample t-test
data: X
t = 40.935, df = 19, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
5.218781 5.781219
sample estimates:
mean of x
5.5
Assumption:
The data are come from normal distribution.
To check this assumption, we draw QQ plot (or quantile-quantile plot) which shows the correlation between a given sample and the normal distribution. A 45-degree reference line is also plotted. QQ plots are used to visually check the normality of the data.
R code:
X=c(5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3,
4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4)
qqnorm(X,lwd=2,col=1)
qqline(X,lwd=2,col=2)
Most of the points are closed to the reference line so normality assumption is valid. This can also be checked via some statistical tests.
R code:
X=c(5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3,
4.9, 5.1, 5.0, 6.0, 6.3, 5.4, 5.3, 5.4)
ks.test(X, "pnorm", mean=mean(X), sd=sd(X))
Output:
One-sample Kolmogorov-Smirnov test
data: X
D = 0.21609, p-value = 0.3078
alternative hypothesis: two-sided
Warning message:
In ks.test(X, "pnorm", mean = mean(X), sd = sd(X)) :
ties should not be present for the Kolmogorov-Smirnov test
Since p nalue>0.05 so normality assumption is
valid.
Question 2. Note that the following problem is similar to scenario E in the previous question....
Computers in some vehicles calculate various quantities related to performance. One of these is the fuel efficiency. For one vehicle equipped in this way, the number of ‘liters per 100 kilometers’ driven were recorded each time the gas tank was filled, and the computer was then reset. Below are the ‘liters per 100 kilometers’ driven for a random sample of 20 of these records. 5.7, 4.6, 6.4, 6.3, 6.9, 5.2, 4.9, 5.4, 4.9, 5.6, 5.4, 5.3, 4.9, 5.1, 5.0, 6.0,...
Question 3. (12 marks) It is posited that babies born at different times of the year may develop the ability to crawl at different ages. Thirty two babies born in January crawled at an average age of 29.75 weeks, with a standard deviation of 7 weeks. Another 32 babies born in August crawled at an average of 33.5 weeks with a standard deviation of 7 weeks. Test whether the posited claim is true. Use α=0.05. Use RStudio or R on...
Question 3. It is posited that babies born at different times of the year may develop the ability to crawl at different ages. Thirty two babies born in January crawled at an average age of 29.75 weeks, with a standard deviation of 7 weeks. Another 32 babies born in August crawled at an average of 33.5 weeks with a standard deviation of 7 weeks. Test whether the posited claim is true. Use α=0.05. Use RStudio or R on Jupyter in...
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Question 1. For each of the following five scenarios, identify (a) the individuals, (b) the type of each variable according to its measurement, (c) the response and explanatory variables and (d) and whether the study is an experiment or an observational study. There is no need to explain your answers. Scenario A. It is posited that babies born at different times of the year may develop the ability to crawl at different ages. Thirty two babies born in January crawled...
INN
MARGIN
ROOMS
NEAREST
OFFICE
COLLEGE
INCOME
DISTTWN
1
61
3203
0.1
549
8
37
12.1
2
34
2810
1.5
496
17.5
39
0.4
3
46
2890
1.9
254
20
39
12.2
4
31.9
3422
1
434
15.5
36
2.7
5
57.4
2687
3.4
678
15.5
32
7.9
6
47.5
3080
2.4
488
13.5
31
6.7
7
54.4
2756
1.1
832
14.5
35
6.9
8
46.2
2244
0.7
496
15.5
38
8.9
9
54.1
2862
1.4
809
16.5
33
3...
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Unless otherwise specified in the problem, you may assume that all solutions are at 25°C. 1. 50.0 mL of a pH 6.00 carbonic acid buffer is titrated with 0.2857 M NaOH, requiring 17.47 mL to reach the second equivalence point. a. Calculate the molarity of carbonic acid and bicarbonate in the original buffer. Carbonic acid: Bicarbonate: b. Calculate the pH of the solution after a total of 100.0 mL of 0.2857...
Value for transmissivity is 185,location is B,flow rate is
20
Question 1: No-flow boundary conditions are implemented by: Question 2: Flow Calculation with no abstraction or recharge m2/day m/day Condition 1 flow is Condition 2 flow is Question 3: Recharge or abstraction at a node is calculated by: Question 4: Water Level and Flows for Condition 1 are: Water level at pumping/recharge node Flow accross boundary AB Flow accross boundary CD ..,..) is m3/dayFlow accross boundary BC m/dayFlow accross boundary...