Scatter Plot and Table

This document provides scatter plots and tables for various questions. It covers topics such as correlation coefficients, significance levels, and statistical analysis. Explore the data and find solutions.

Question 1
(a) Scatter plot
2.5 3 3.5 4 4.5 5
0
2
4
6
8
10
12
Scatter Plot
x (magnitude of an earthquak richter scale)
y (depth (km)
(b) Table
All values are correct.
r =0.53 2
Option c
Given our value of r, y should tend to increase as x increases.
Question 2
(a) Scatter plot
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(b) Table
All values are correct.
r =0.930
Option c
Given our value of r, y should tend to increase as x increases.
Question 3
(a) Scatter plot
2

(b) Table
r =0.997
(c) x ¯¿ 16.00
y ¯¿ 101.50
y=24.902+(4.787∗X )
(d) Option a
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(e) Values
(f) X =20
y=24.902+ ( 4.787∗X )
Y =24.902+ ( 4.787∗20 )=120.65 kg
Question 4
(a) Scatter plot
(b) Table
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r =0.920
(c) x ¯¿ 62.00
y ¯¿ 18.33
y=−28.432+(0.754∗X )
(d) Option a
(e) Values
(f) X =70 year old
y=24.902+ ( 4.787∗X )
Y =−28.432+ ( 0.754∗7 0 )=24.35 %
Question 5
(a) Level of significance = 1%
Option b
5

(b) Chi square = 12.656
Are all the expected frequencies greater than 5? = Yes
Chi square
Degree of freedom = (4-1) (5-1) = 12
(c) P value = 0.395
Option a
P value > 0.100
(d) Option a
Since the P-value > α, we fail to reject the null hypothesis.
(e) Option b
At the 1% level of significance, there is insufficient evidence to conclude that contribution
level and ethnic group are not independent.
Question 6
(a) Level of significance = 1%
Option a
(b) Chi square = 0.667
Are all the expected frequencies greater than 5? = Yes
Option a: Chi square
Degree of freedom = (5-1) = 4
(c) P value = 0.9553
Option a
P value > 0.100
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(d) Option a
Since the P-value > α, we fail to reject the null hypothesis.
(e) Option b
At the 0.01 level of significance, the evidence is sufficient to conclude that the regional
distribution of raw materials does not fit the distribution at the current excavation site.
Question 7
(a) Level of significance = 0.10
Option 1
(b) Chi square = ( 9−1 )∗110.6
136.2 =6.50
Degree of freedom = 9-1 = 8
Option b: We assume a normal population distribution.
(c) The p value = 0.5914
Option a
P value > 0.100
(d) Option a
Since the P-value > α, we fail to reject the null hypothesis.
(e) Option a
At the 1% level of significance, there is insufficient evidence to conclude that the variance for
number of mountain climber deaths is less than 136.2
(f) Confidence interval
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Xu=1−0.90
2 =0.05 , degree of freedom=8 , X2 u=15.507
X L= 1+0.90
2 =0. 9 5 , degree of freedom=8 , X2 u=2.733
Lower limit = sqrt {(n-1)*s^2 / Xu^2} = sqrt { (9-1)*110.6/15.507} = 7.55
Upper limit = sqrt{(n-1)*s^2 / XL^2} =sqrt{ (9-1)*110.6/2.733}= 17.99
Option a
We are 90% confident that σ2 lies within this interval.
Question 8
(a) Level of significance = 0.05
Option d
(b) F stat = 2.087/1.214 = 1.72
DfN = 21-1 = 20
DfD = 18-1 = 17
Option a
The populations follow independent normal distributions. We have random samples from
each population.
(c) The p value = 0.1315
Option b
0.100 < p-value < 0.200
(d) Option c
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not
statistically significant.
(e) Option d
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Fail to reject the null hypothesis, there is insufficient evidence that the variance in percentage
yields on assets is different in both companies.
Question 9
(i) Level of significance = 0.01
Option d
(ii) Chi square stat = 6.620
(iii) The p value = 0.085
Option b
0.050 < P-value < 0.100
(iv) Option c
Since the P-value is ≥ α, we do not reject the null hypothesis.
(v) Option a
At the 1% level of significance, there is insufficient evidence to claim that time to do a test
and test results are not independent.
Question 10
(i) Level of significance = 0.01
Option d
(ii) Test statistics = (15-1)*(0.36)^2 / (0.23)^2 = 34.30
(iii) The p value = 0.00186
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Option f
P value < 0.005
(iv) Option b
Since the P-value < α, we reject the null hypothesis.
(v) Option a
At the 1% level of significance, there is sufficient evidence to conclude that the variance has
increased and the machine needs to be adjusted.
Question 11
(i) Level of significance = 0.01
Option b
(ii) Test statics (chi square) = 10.65
(iii) The p value = 0.03079
Option c
0.025 < P-value < 0.050
(iv) Option c
Since the P-value ≥ α, we do not reject the null hypothesis.
(v) Option a
At the 1% level of significance, there is insufficient evidence to claim that the age
distribution of the population of Blue Valley has changed.
Question 12
Option 5
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F test for two variances
(i) Level of significance = 0.05
Option a
(ii) F stat = 0.212 / 0.15 = 1.41
(iii) The p value = 0.217
Option a
P-value > 0.200
(iv) Option a
Since the P-value is greater than or equal to the level of significance α = 0.05, we fail to
reject the null hypothesis.
(v) Option c
At the 5% level of significance, there is insufficient evidence to show that the variance for the
new manufacturing process is not different.
Question 13
Since the scatter diagram shows no linear relationship, the correlation coefficient r=0.
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