A trainer was asked to give a lecture on population profiles in different Local Authorities (LAs) in the UK Using data from the 2011 census, he created the following scatter diagram for 17 selected LAs. 17 Selected Local Authorities 0.25- 0.- 0.15- 0.1- 0.05- 0+ 0.b5 o.1 o.1s 02 0.25 03 0.35 Proportion aged 65+ He selected the 17 LAs using the following method. The proportions of people aged 18 to 24 and aged 65+ in any Local Authority are denoted by Proung and Pnior respectively. The trainer used a spreadsheet to calculate the value of k = for each of the 348 LAs in the UK. He then used specific ranges of values of k to select the 17 LAs. (a) Estimate the ranges of values of k that he used to select these 17 LAs. (b) Using the 17 LAs the trainer carried out a hypothesis test with the following hypotheses. and P H: There is no linear correlation in the population between Pyoung H: There is negative linear correlation in the population between P young and P senior senior He found that the value of Pearson's product-moment correlation coefficient for the 17 LAS is -0.797, correct to 3 significant figures. ) Use the table on page 9 to show that this value is significant at the 1% level. The trainer concluded that there is evidence of negative linear correlation between P, Penior in the population. and young (ii) Use the diagram to comment on the reliability of this conclusion Proportion aged 18 to 24
A trainer was asked to give a lecture on population profiles in different Local Authorities (LAs) in the UK Using data from the 2011 census, he created the following scatter diagram for 17 selected LAs. 17 Selected Local Authorities 0.25- 0.- 0.15- 0.1- 0.05- 0+ 0.b5 o.1 o.1s 02 0.25 03 0.35 Proportion aged 65+ He selected the 17 LAs using the following method. The proportions of people aged 18 to 24 and aged 65+ in any Local Authority are denoted by Proung and Pnior respectively. The trainer used a spreadsheet to calculate the value of k = for each of the 348 LAs in the UK. He then used specific ranges of values of k to select the 17 LAs. (a) Estimate the ranges of values of k that he used to select these 17 LAs. (b) Using the 17 LAs the trainer carried out a hypothesis test with the following hypotheses. and P H: There is no linear correlation in the population between Pyoung H: There is negative linear correlation in the population between P young and P senior senior He found that the value of Pearson's product-moment correlation coefficient for the 17 LAS is -0.797, correct to 3 significant figures. ) Use the table on page 9 to show that this value is significant at the 1% level. The trainer concluded that there is evidence of negative linear correlation between P, Penior in the population. and young (ii) Use the diagram to comment on the reliability of this conclusion Proportion aged 18 to 24
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A trainer was asked to give a lecture on population profiles in different Local Authorities (LAs) in
the UK Using data from the 2011 census, he created the following scatter diagram for 17 selected
LAs.
17 Selected Local Authorities
0.25-
0.2-
0.15-
0.1-
0.05-
0-
0.05 o.1 o.is 02 0.25 o3 0.35
Proportion aged 65+
He selected the 17LAS using the following method. The proportions of people aged 18 to 24 and
aged 65+ in any Local Authority are denoted by Pyoung and Pior Tespectively. The trainer used a
spreadsheet to calculate the value of k = for each of the 348 LAs in the UK. He then used
specific ranges of values of k to select the 17 LAs.
(a) Estimate the ranges of values of k that he used to select these 17 LAs.
(b) Using the 17 LAs the trainer camied out a hypothesis test with the following hypotheses.
H: There is no linear correlation in the population between Pyoung
H. There is negative linear correlation in the population between P,
and Pserior
young
and P.
senior
He found that the value of Pearson's product-moment correlation coefficient for the 17 LAs
is -0.797, corect to 3 significant figures.
@ Use the table on page 9 to show that this value is significant at the 1% level.
The trainer concluded that there is evidence of negative linear correlation between P,
Penior in the population.
and
young
(i) Use the diagram to comment on the reliability of this conclusion.
Proportion aged 18 to 24
Transcribed Image Text:(c) Describe one outstanding feature of the population in the areas represented by the points in the
bottom right hand comer of the diagram
(d) The trainer's audience included representatives from several universities.
Suggest a reason why the diagram might be of particular interest to these people.
Critical values of Pearson's product-moment correlation coefficient
1-tail test
5%
2.5%
5%
0.5%
1%
2-tail test
10%
2%
1%
0.9877
0.9969
0.9995
0.9999
4
0.9000
0.9500
0.9800
0.9900
5
0.8054
0.7293
0.6694
0.8783
0.8114
0.7545
0.7067
0.9343
0.8822
0.8329
0.7887
0.9587
0.9172
6.
7.
0.8745
0.6215
0.8343
0.6664
0.6319
0.6021
0.5760
9
0.7498
0.5822
0.5494
0.7977
10
0.7155
0.7646
0.7348
11
12
0.5214
0.4973
0.6851
0.6581
0.7079
0.6835
13
0.4762
0.5529
0.6339
14
0.4575
0.5324
0.6120
0.6614
0.4409
0.4259
15
0.6411
0.5140
0.4973
0.5923
16
0.5742
0.6226
0.5577
0.5425
0.5285
0.5155
0.5034
17
18
0.4124
0.4000
0.4821
0.4683
0.6055
0.5897
19
0.3887
0.4555
0.5751
20
0.3783
0.4438
0.5614
21
0.3687
0.3598
0.3515
0.4329
0.5487
22
23
0.4227
0.4132
0.4921
0.4815
0.5368
0.5256
24
0.3438
0.4044
0.4716
0.5151
25
0.3365
0.3961
0.3882
0.3809
0.4622
0.4534
0.4451
0.5052
0.4958
26
0.3297
27
0.3233
0.3172
0.3115
0.3061
0.4869
0.4785
0.4705
28
29
0.3739
0.3673
0.4372
0.4297
0.4226
30
0.3610
0.4629
123
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