Question

6 and 7. Listed below are heights (inches) and shoe length (inches) of 12 women. Use a 0.05 significance level to test the claim that there is a linear correlation between heights and shoe length.

Height       67 66 64 64 67 64 68 65 68 65 66 61

Shoe Length 10 7 7 9 8 8.5 8.5 8.5 9 8 7.5 6

USE A 0.05 SIGNIFICANCE LEVEL TO TEST THE CLAIM:

H0: ρ = 0

H1: ρ ≠ 0

Test Statistic: r =_________ Q24(ROUND TO 3 DECIMAL PLACES)

P-value: p=___________Q25(ROUND TO 4 DECIMAL PLACES)

Decision/Conclusion: _________________________________Q26(CIRCLE ONE BELOW) Reject H0, There is sufficient evidence to warrant the rejection of the claim that there is a linear correlation.

OR

Fail to Reject H0, There is not sufficient evidence to warrant the rejection of the claim that there is a linear correlation.

FIND THE REGRESSION EQUATION: y = a + bx

a =_____________ Q27(ROUND TO 2 DECIMAL PLACES)

b =_____________ Q28(ROUND TO 2 DECIMAL PLACES)

FIND THE BEST PREDICTED SHOE LENGTHFOR A HEIGHTOF 63: _________________Q29(ROUND TO WHOLE NUMBER)

Answer 1

SOLUTION :

Height (x) and shoe length (y) is given

Now we find,

.   . . n=12

. S.D.(

. S.D.()= 1.03

.

.   

Corr(x,y)=0.585

test statistic,

  

Test statistic r = 2.280

P value : 0.0457 .............( From table critical value of t distribution with n-2 df and alpha is 0.05)

Decision : Pvalue < alpha. Reject Ho.

conclusion : There is sufficient evidence to conclude that claim that the linear relationship between height and shoe length.

  

The regression equation is y= a+bx

=

a= = -12.43

The regression equation is y = -12.43+0.31*x

Shoe length for a height is 63 the

y= -12.43+0.31*63

y= 7.32

Best predicted shoe length fora height 63 is 7.32.

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