1. A manufacturer of infant formula is running anexperiment using the standard (
ID: 2951242 • Letter: 1
Question
1. A manufacturer of infant formula is running anexperiment using the standard (control) formulation and two newformulations, A and B. The goal is to boost the immune system inyoung children. There are 120 children in the study, and they arerandomly assigned, 40 to each of the three feeding groups. Thestudy is run for twelve weeks. The variable measured is Total IGAin mg per dl. It is measured at the end of the study, with highervalues being more desirable. We are going to run a one-way ANOVA onthese data. The ANOVA table is given below.
Source
DF
SS
MS
F
Group
2
0.02357
0.01179
4.68
Error
117
0.29484
0.00252
Total
119
0.31841
(a) The hypotheses tested by the one-way ANOVA F test are
A. : the mean IGA score is the same for allthree formulas. : the mean IGA score is higher for both treatmentgroups than the control.
B. : the mean IGA score is the same for allthree formulas. : the mean IGA score is higher for at least one ofthe two treatment groups than the control.
C. : the mean IGA score is the same for allthree formula. : the mean IGA score is not the same for all threeformulas.
(b) The denominator degrees of freedom for the ANOVA F statisticfor testing the hypothesis in part (a) is
A. 2.
B. 117.
C. 119.
(c) The P-value for testing the hypothesis in part (a) is
A. less than 0.001.
B. between 0.001 and 0.025.
C. greater than 0.10.
(d) At the 0.05 level of significance, the following decisioncan be made:
A. The null hypothesis is rejected.
B. We fail to reject the null hypothesis.
C. The data do not provide enough informationand no decision can be made.
Source
DF
SS
MS
F
Group
2
0.02357
0.01179
4.68
Error
117
0.29484
0.00252
Total
119
0.31841
Explanation / Answer
a) A. : the mean IGA score is the same for all three formulas.: the mean IGA score is higher for both treatment groups than thecontrol.b) B. 117.
c) B. between 0.001 and 0.025.
d) A. The null hypothesis is rejected.
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