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Nutrition
Researchers compared protein intake among three groups of postmenopausal women: (1) women eating a standard American diet (STD), (2) women eating a lacto-ovo-vegetarian diet (LAC), and (3) women eating a strict vegetarian diet (VEG). The
Perform a statistical procedure to compare the means of the three groups using the critical-value method.
Table 12.29 Protein intake (mg) among three dietary groups of postmenopausal women
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Conduct the test to compare the means of the three groups using critical value method.
Answer to Problem 1P
There is sufficient evidence to conclude that there is a significant difference between the means of the three groups at 5% level of significance.
Explanation of Solution
Hypotheses for the test is given below:
Null hypothesis:
Alternative hypothesis:
There are 3 groups and 26 observations.
That is,
The means sum of squares are as follows:
The sum of squares is calculated as follows:
The test statistic for the test is calculated as given below:
Critical value:
Consider the level of significance as 0.05.
The numerator degrees of freedom is 2 and the denominator degrees of freedom is 23.
Software procedure:
Step-by-step procedure to obtain critical value using Excel software:
- Open Excel sheet.
- Enter the formula, “=F.INV(0.95,2,23)” in cell A1.
- Click Enter.
Output using Excel software is given below:
Thus, the F-critical value is 3.42.
Decision based on critical value:
Reject the null hypothesis H0 if, if F> F-critical value;
Otherwise fail to reject H0.
Conclusion:
Here, F(=10.23)> F-critical value (=3.42).
Therefore, the null hypothesis is rejected.
Thus, there is sufficient evidence to conclude that there is a significant difference between the means of the three groups at 5% level of significance.
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Chapter 12 Solutions
Fundamentals of Biostatistics
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