Question

A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants, while the infants in another group were fed a standard baby formula without any iron supplements. Here are summary results on blood hemoglobin levels at 12 months of age.

Group n x s

Breast-fed    22    13.1 1.6

Formula 19 12.6 1.7

Carry out a t test. Give the P-value. (Use ? = 0.01. Use ?_breast-fed ? ?_formula. Round your value for t to three decimal places, and round your P-value to four decimal places.)

t=____

pvalue=_____

(b)Give a 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants. (Round your answers to three decimal places.)

(    ,    )

Answer 1

Let sample 1 is sample of breast fed and sample 2 is sample of formula.

The hypothesis are

H0: - = 0 v/s H1:   -   0

The test statistic is

Where,

  

= 1.65

Hence,

= 0.968

df = n1 + n2 - 2= 22 + 19 - 2 = 39

p value = 2* p ( t < 0.968 ) = 2 * 0.1695 = 0.3390

Here p value > ( 0.01 )

Hence we failed to reject null hypothesis.

Conclusion : There is no difference in mean hemoglobin level between the two populations of infants.

b) The 95% confidence interval is given by

{ ( ) - E , ( ) + E }

Where,

c = 0.95 ,

df = n1 + n2 - 2= 22 + 19 - 2 = 39

tc =

= 1.045

Hence the confidence interval is

{ ( 13.1 - 12.6 ) - 1.045 , ( 13.1 - 12.6 ) + 1.045 }

( -0.545 , 1.545 )

Here confidence interval includes 0.

Hence we conclude that there is no difference in mean hemoglobin level between the two populations of infants.