Question

10. A study of iron deficiency among infants compared samples of infants following different feeding regimens. One group contained breast-fed infants and the other group was fed a baby formula with iron supplements. Here are the summary results on blood hemoglobin levels at 12 months of age. Group n Sample mean Sample St. Dev. Breast-fed 23 13.3 1.7 Formula 19 12.4 Does the data provide evidence at the 10% level that the hemoglobin levels differ for these two populations of infants? YOU NEED ONLY STATE YOUR HYPOTHESES FOR THIS QUESTION (and define your parameter(s).) 1.8 11. A significance test is done to determine if there is a positive correlation between H:p=0 college GPA and salary for first job. The hypotheses were H:p>0. If the p-value for the test was p=0.001, give the conclusion for the significance test. 12. What is ANOVA used for?

Answer 1

10. The hypothesis we are testing here is:

Ho: There is no difference in the means for the two groups vs Ha: The means are difference for two groups

Here we assume that the population variances of the two groups are equal. Then we apply the two-sample t-test for testing the above hypothesis.

First, the pooled variance is given by:

$\small S_p^2=\frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}=3.0475$. Now using this we will find the test statistic.

$\small t=\frac{\bar{x}_1-\bar{x}_2}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}=1.663$. While the critical value at the level of significance of 10% is 1.684. Thus the test statistic is less than the critical value. Hence we fail to reject the null hypothesis.

11. Ig the significance level is more than 0.001. Then we conclude that there is sufficient evidence to support the claim that there is a positive linear relationship between the two variables.

12. When we want to test the equality of more than two means we should use ANOVA.