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 13.3 1.7

Formula 18 12.4 1.8

(a) Is there significant evidence that the mean hemoglobin level is higher among breast-fed babies? State H0 and Ha.

H0: μbreast-fed = μformula; Ha: μbreast-fed > μformula

H0: μbreast-fed < μformula; Ha: μbreast-fed = μformula

H0: μbreast-fed > μformula; Ha: μbreast-fed = μformula

H0: μbreast-fed ≠ μformula; Ha: μbreast-fed < μformula

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

t =

P-value =

What is your conclusion?

Reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Fail to reject the null hypothesis. There is significant evidence that the mean hemoglobin level is higher among breast-fed babies.

Fail to reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

(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.) ,

(c) State the assumptions that your procedures in (a) and (b) require in order to be valid.

We need sample sizes greater than 40.

We need the data to be from a skewed distribution.

We need two independent SRSs from normal populations.

We need two dependent SRSs from normal populations.

Answer 1

(a) right choice is H0: μbreast-fed = μformula; Ha: μbreast-fed > μformula,

here we want to test the evidence that the mean hemoglobin level is higher among breast-fed babies so alternate hypothesis would be Ha: μbreast-fed > μformula and

null hypothesis would be no preferences between μbreast-fed and  μformula or

H0: μbreast-fed = μformula,

(b) here we use t-test with

null hypothesis H0:null hypothesis H0:µ1=µ2 and alternate hypothesis H1: µ1>µ2 ( this is right-one-tailed test)

statistic t=|(mean1-mean2)|/((s_p*(1/n1 +1/n2)^1/2) =1.6224

with df is n=n1+n2-2 and s_p²=((n1-1)s1²+(n2-1)s2²)/n

one tailed p-value=0.0565

Fail to reject the null hypothesis. There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies.

(b)

(1-alpha)*100% confidence interval for difference population mean= difference sample mean±t(alpha/2,n)*SE(difference)

95% confidence interval =0.9±t(0.05/2,38)*0.5547==0.9±2.0244*0.5547=0.9±1.223=(-0.-323, 2.123)

(c)We need two independent SRSs from normal populations.

following information has been generated for answering the above

	sample	mean	s	s2	n	(n-1)s2
	breast-fed	13.3000	1.7000	2.8900	22	60.6900
	formula	12.4000	1.8000	3.2400	18	55.0800
	difference=	0.9000	sum=	6.1300	40	115.7700
	sp2=	3.0466
	sp=	1.7454
	SE=	0.5547
	t=	1.6224
one tailed	p-value=	0.0565
two tailed	p-value=	0.1130