Question

A small study is conducted involving 10 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams.:

Gestational age: 34.7, 36, 29.3, 40.1, 35.9, 40.8, 38.3, 37, 41.2, 39.8.

Birth weight:1895, 2030, 1440, 2835, 3115, 4013, 3174, 3625, 2289, 2845.

a) Find the correlation coefficient of the gestational age at birth and birth weight.

b) Test H0:ρ= 0 vs.H1:ρ does not equal 0. at 5% level of significance. Here ρ is the population correlation coefficient between the two variables. Use P(t8>2.36) = 0.025.

c) Construct a regression lineY=β0+β1X+, where Y,X are gestational age at birth and birth weight respectively. What are the best estimates of β0 and β1?

d) Test H0:β1= 0 vs. H1:β1 not equal 0 at 5% level of significance.

e) Compute the coefficient of determination,R^2.

Answer 1

BY USING MS EXCEL WE HAVE

r= 0.6257

b) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Level of significance =0.05

Test statistics= r*sqrt(n-2)/sqrt(1-r^2)

= 0.6257*sqrt(8)/sqrt(0.6085)

= 0.6257*2.83/0.78

t= 2.27

Critical value of t= 2.36

P value= 0.025

Since P value SMALLER THAN 0.05

DECISION: REJECT H0.

c) By using EXCEL

d) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

Test statistic t= 2.27

P value= 0.053

Since P value>0.05 therefore NOT SIGNIFICANT

DECISION: DO NOT REJECT H0.

e) Coefficient Of determination R squared=0.3915