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	23	13.3	1.7
Formula	18	12.6	1.8

(a)

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

____H₀: μ_breast-fed > μ_formula;   H_a: μ_breast-fed = μ_formula

_{_____H0}: μ_breast-fed < μ_formula;   H_a: μ_breast-fed = μ_formula  

____H₀: μ_breast-fed ≠ μ_formula;   H_a: μ_breast-fed < μ_formula

____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?

____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 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.

(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.)

________, _________ Answers

__C)

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

____We need two dependent SRSs from normal populations.

____We need sample sizes greater than 40.  

____ We need two independent SRSs from normal populations.

_____We need the data to be from a skewed distribution.

Answer 1

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	23	13.3	1.7
Formula	18	12.6	1.8

(a)

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

____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	=	1.275
P-value	=	0.1049

What is your conclusion?

____ 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.)

( -0.410, 1.810 )

__C)

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

____ We need two independent SRSs from normal populations.

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.01
Population 1 Sample
Sample Size	23
Sample Mean	13.3
Sample Standard Deviation	1.7
Population 2 Sample
Sample Size	18
Sample Mean	12.6
Sample Standard Deviation	1.8
Intermediate Calculations
Population 1 Sample Degrees of Freedom	22
Population 2 Sample Degrees of Freedom	17
Total Degrees of Freedom	39
Pooled Variance	3.0426
Standard Error	0.5489
Difference in Sample Means	0.7000
t Test Statistic	1.2752
Upper-Tail Test
Upper Critical Value	2.4258
p-Value	0.1049
Do not reject the null hypothesis

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	95%
Intermediate Calculations
Degrees of Freedom	39
t Value	2.0227
Interval Half Width	1.1103
Confidence Interval
Interval Lower Limit	-0.4103
Interval Upper Limit	1.8103