The correlation coerficient r is a sample statistic. W correlation coefficient e (Greek letter rho)? You do not khow hoW there is a quick way to determine if the sample evidence based on p is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if pa 0. We do this by comparing the value Jrl to an entry in the correlation table. The value of a in the table gives us the probability of concluding that p +0 when, in fact, p= 0 and there is no population correlation. We have two choices for a: a = 0.05 or a = 0.01. nat does it tell us about the value of the population Critikal Values for Correlation Coeffident r -0.05 0.01 .0.05 G-0.01 a0.05 -0.01 1.00 1.00 13 053 0.68 23 0.41 0.53 4 0.95 099 14 0.53 0.66 24 0.40 0.52 0.88 0.96 15 051 0.64 25 0.40 051 0.81 092 16 0.50 0.61 26 0.39 0.50 0.75 0.87 17 0.48 0.61 27 0.38 0.49 0.71 083 18 0.47 0.59 28 0.37 0.48 067 080 19 0.46 0.58 29 0.37 0.47 10 0.63 0.76 20 044 0.56 30 0.36 0.46 11 0.60 0.73 21 043 0.55 12 0.58 0.71 22 0.42 0.54 (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of Irl large enough to conclude that weight and age of Shetland ponies are correlated? Use a = 0.05. (Round your answer for r to four decimal places.) x 3 y 60 12 23 172 19 190 95 140 A USE SALT critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. O Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. (b) Look at the data below regarding the variables x lowest barometric pressure as a cyclone approaches and y- maximum wind speed of the cyclone. Is the value of Ir| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use a- 0.01. (Round your answer for r to four decimal places.) x 1004 y 40 974 69 930 149 975 992 935 100 65 145 critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
The correlation coerficient r is a sample statistic. W correlation coefficient e (Greek letter rho)? You do not khow hoW there is a quick way to determine if the sample evidence based on p is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if pa 0. We do this by comparing the value Jrl to an entry in the correlation table. The value of a in the table gives us the probability of concluding that p +0 when, in fact, p= 0 and there is no population correlation. We have two choices for a: a = 0.05 or a = 0.01. nat does it tell us about the value of the population Critikal Values for Correlation Coeffident r -0.05 0.01 .0.05 G-0.01 a0.05 -0.01 1.00 1.00 13 053 0.68 23 0.41 0.53 4 0.95 099 14 0.53 0.66 24 0.40 0.52 0.88 0.96 15 051 0.64 25 0.40 051 0.81 092 16 0.50 0.61 26 0.39 0.50 0.75 0.87 17 0.48 0.61 27 0.38 0.49 0.71 083 18 0.47 0.59 28 0.37 0.48 067 080 19 0.46 0.58 29 0.37 0.47 10 0.63 0.76 20 044 0.56 30 0.36 0.46 11 0.60 0.73 21 043 0.55 12 0.58 0.71 22 0.42 0.54 (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of Irl large enough to conclude that weight and age of Shetland ponies are correlated? Use a = 0.05. (Round your answer for r to four decimal places.) x 3 y 60 12 23 172 19 190 95 140 A USE SALT critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. O Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. (b) Look at the data below regarding the variables x lowest barometric pressure as a cyclone approaches and y- maximum wind speed of the cyclone. Is the value of Ir| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use a- 0.01. (Round your answer for r to four decimal places.) x 1004 y 40 974 69 930 149 975 992 935 100 65 145 critical r Conclusion O Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. O Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
Problem 18HP
Related questions
Question
Transcribed Image Text:The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient p (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of p yet. However,
there is a quick way to determine if the sample evidence based on p is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if p + 0. We do
this by comparing the value Ir| to an entry in the correlation table. The value of a in the table gives us the probability of concluding that p + 0 when, in fact, p = 0 and there is no population correlation. We have two choices for a: a =
0.05 or a = 0.01.
Critical Values for Correlation Coefficdent r
a = 0.05
a = 0.01
a = 0.05
a = 0,01
a = 0.05
a = 0.01
3
1.00
1.00
13
0.53
0.68
23
0.41
0.53
4
0.95
0.99
14
0.53
0.66
24
0.40
0.52
0.88
0.96
15
0.51
0.64
25
0.40
0.51
6.
0.81
0.92
16
0.50
0.61
26
0.39
0.50
7
0.75
0.87
17
0.48
0.61
27
0.38
0.49
0.71
0.83
18
0.47
0.59
28
0.37
0.48
9.
0.67
0.80
19
0.46
0.58
29
0.37
0.47
10
0.63
0.76
20
0.44
0.56
30
0.36
0.46
11
0.60
0.73
21
0.43
0.55
12
0.58
0.71
22
0.42
0.54
0.05.
(a) Look at the data below regarding the variables x =
(Round your answer for r to four decimal places.)
age of a Shetland pony and y = weight of that pony. Is the value of Ir| large enough to conclude that weight and age of Shetland ponies are correlated? Use a =
3
6.
12
23
19
60
95
140
172
190
A USE SALT
critical r
Conclusion
Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.
O Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.
Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.
O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.
(b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric
pressure and wind speed of a cyclone are correlated? Use a = 0.01. (Round your answer for r to four decimal places.)
1004
975
992
935
974
930
40
100
65
145
69
149
critical r
Conclusion
O Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
O Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
Transcribed Image Text:12
0.58
0.71
22
0.42
0.54
(a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use a =
(Round your answer for r to four decimal places.)
0.05.
%3D
12
23
19
60
95
140
172
190
A USE SALT
critical r
Conclusion
O Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.
Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.
O Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated.
O Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated.
maximum wind speed of the cyclone. Is the value of Ir| large enough to conclude that lowest barometric
(b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y
0.01. (Round your answer for r to four decimal places.)
pressure and wind speed of a cyclone are correlated? Use a =
1004
975
992
935
974
930
40
100
65
145
69
149
r
critical r
Conclusion
Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
O Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
O Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
O Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.
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