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	24	13.1	1.6
formula	20	12.5	1.7

(a)

bIs there significant evidence that the mean hemoglobin level is higher among breast-fed babies? State H₀ and H_a.

a. H₀: μ_breast-fed < μ_formula;   H_a: μ_breast-fed = μ_formula

b. H₀: μ_breast-fed ≠ μ_formula;   H_a: μ_breast-fed < μ_formula   

c.  H₀: μ_breast-fed = μ_formula;   H_a: μ_breast-fed > μ_formula

d. H₀: μ_breast-fed > μ_formula;   H_a: μ_breast-fed = μ_formula

Carry out a t test. Give the P-value. (Use α = 0.01. Use μ_breast-fed − μ_formula. 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?

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

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

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

d. Fail to reject the null hypothesis. There is 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 the data to be from a skewed distribution.

We need sample sizes greater than 40.    

We need two independent SRSs from normal populations.

We need two dependent SRSs from normal populations
.

Answer 1

(a) The correct null and alternative hypothesis for the hypothesis test is:

the mean hemoglobin level for two groups are not different.

the mean hemoglobin level for infants with breast feeding is higher than the mean hemoglobin level of infant those fed with a formula.

Test-statistic: ; with degrees of freedom,

where, pooled variance

sample mean for Breast-fed group

population mean for Breast-fed

sample mean for Formula group

population mean for Formula

sample standard deviation for Breast-fed group.

sample standard deviation for Formula group.

sample size for Breast-fed group and Formula group.

Given:

Groups	Breast-fed	Formula
Sample mean
sample standard deviation
sample size

Calculation for test-statistic:

The test-statistic is calculated as

P-value:

Conclusion:

The correct option is (a) ,i.e., "We fail to reject the null hypothesis, H₀ . There is not significant evidence that the mean hemoglobin level is higher among breast-fed babies."

The level of significance is given as and the we have calculated the .

Since,

So, at the sample data does not provide enough evidence to support the alternative hypothesis, H_a .

Hence we conclude that, we did not find evidence that ,the mean hemoglobin level for infants with breast feeding is higher than the mean hemoglobin level of infant those fed with a formula.

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(b) Calculation for the 95% confidence inter for the mean difference :

for 95% confidence interval :

and

So, the 95% confidence interval for the mean difference in hemoglobin level between two populations of infant is calculated as , i.e.,

But, since the confidence interval (-0.406, 1.606) contains 0, so we cannot conclude that the mean hemoglobin level is higher among breast-fed babies.

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(c) Assumptions:

• We need two independent SRSs from the normal populations.
• Groups are to be independent.
• Individual observations should to be independent.