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	13.2	1.6
Formula	18	12.4	1.7

(a)

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

H₀: μ_breast-fed > μ_formula;   H_a: μ_breast-fed = μ_formulaH₀: μ_breast-fed < μ_formula;   H_a: μ_breast-fed = μ_formula     H₀: μ_breast-fed ≠ μ_formula;   H_a: μ_breast-fed < μ_formulaH₀: 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?

Fail to 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 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.

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 two independent SRSs from normal populations.     

We need two dependent SRSs from normal populations.

We need the data to be from a skewed distribution.

Answer 1

Solution:-

a)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u_{Breast feed}< u_Formula
Alternative hypothesis: u_{Breast feed} > u_Formula

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.52623
DF = 38
t = [ (x₁ - x₂) - d ] / SE

t = 1.52

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 1.52

Therefore, the P-value in this analysis is 0.068

Interpret results. Since the P-value (0.068) is greater than the significance level (0.01 ), we failed to reject the null hypothesis.

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

b) 95% confidence interval for the mean difference in hemoglobin level between the two populations of infants is C.I = ( 0.266, 1.866).

C.I = 0.80 + 2.025*0.52623

C.I = 0.80 + 1.0656

C.I = ( 0.266, 1.866)

c) We need two independent SRSs from normal populations.