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 p0. We do this by comparing the value Irl 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 Coefdentr n- 0.05 . - 0.01 n a-0.05 a- 0.01 n a-0.05 a- 0.01 3 1.00 1.00 13 053 068 23 041 053 4 0.95 099 14 053 0.66 24 040 052 0.88 096 IS 051 0.64 25 0.40 0.81 092 16 0.50 0.61 26 0.39 0.50 7 0.75 087 17 0.48 27 0.38 049 0,71 083 18 047 0.59 28 0.37 0.48 0.67 080 19 0.46 0.58 29 0.37 047 10 0.63 0.76 20 044 0.56 30 0.36 046 11 0.60 0.73 21 043 055 12 0.58 8 071 22 042 054 (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 forr to four decimal places.) 36 12 y 60 19 17 186 95 140 176 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.

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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The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient ? (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of ? yet. However, there is a quick way to determine if the sample evidence based on ? 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 ? ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of ? in the table gives us the probability of concluding that ? ≠ 0 when, in fact, ? = 0 and there is no population correlation. We have two choices for ?: ? = 0.05 or ? = 0.01.

The correlation coefficientr 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 ofp 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 r| 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 Coefficient r
x = 0.05
= 0.01
a = 0.05
a = 0.01
x = 0.05 x = 0.01
n
n
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
8
0.71
0.83
18
0.47
0.59
28
0.37
0.48
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
(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 = 0.05. (Round your answer for r to four
decimal places.)
%3D
X
3
6
12
19
17
y
60
95
140
176
186
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 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
972
934
y
40
100
65
145
65
154
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.
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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