the body mass index is a popular measure for determining a persons healthy body
ID: 3156158 • Letter: T
Question
the body mass index is a popular measure for determining a persons healthy body weight for their height. using a random sample of 684 women from the US population of women in the age range of 20-29, the sample mean BMI is found to be 26.8, and the sam standard deviation is found to be 7.42. use an appropriate model to conduct a hypothesis test to see whether there is enough evidence to conclude that the true mean BMI of all the US population of women in that age group is less than 27. use a significance level of a=0.05 answer the following: write the null hypothesis: write the alternative hypothesis: test statistic: p-value: conclusion:
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u >= 27
Ha: u < 27 [ANSWER, HYPOTHESES]
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As we can see, this is a left tailed test.
Getting the test statistic, as
X = sample mean = 26.8
uo = hypothesized mean = 27
n = sample size = 684
s = standard deviation = 7.42
Thus, z = (X - uo) * sqrt(n) / s = -0.704943225 [ANSWER, TEST STATISTIC]
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Also, the p value is,as this is left tailed,
p = 0.240422784 [ANSWER, P VALUE]
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As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
There is no significant evidence to conclude that the true mean BMI of all the US population of women in that age group is less than 27 at 0.05 level. [CONCLUSION]
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