You have been asked to design a study to test whether a new, healthy lunch progr
ID: 3223580 • Letter: Y
Question
You have been asked to design a study to test whether a new, healthy lunch program is affecting 7th graders weight. To address the research objective you decide to test whether the average weight is lower than the expected weight of 7th graders, 100 lbs. You performed a sample size calculation (alpha= 0.05, beta= 0.01, sigma=15 and difference =15) and arrived at needing at least 54 students. You report your finding to the school principal who informs you that there is only enough money in the budget to study 30 students. Discuss two aspects of your sample size calculation you could adjust to reduce the sample size. Increase the meaningful difference that you will be able to detect. Decrease the power of the test. The power is currently set to 0.99 which is very high. It is reasonable to decrease this to 0.90 and even o.80. You do not want to adjust sigma if it is an accurate estimate of variability. Lowering it to generate a smaller sample size would underpower the study. The study involves testing the following hypothesis: H_o:mu=100 vs. H_a:muExplanation / Answer
Answer to question# 1)
The two aspects that influence the sample size are as follows:
1. Increase Type II error (Beta)
We know the the higher the sample size the better results we get , this implies it increases the power of the test
Thus if we wish to reduce the sample size, we need to compromise with the power of the test
the power of the test is given by 1- Beta
Thus if we increase the value of Beta , we can definitely reduce the sample size
.
2. Increase Type I error (Alpha)
The second aspect is that if we wish to increase the confidence level c , we need a larger sample. Confidence level c = 1- alpha. Thus if we look for a smaller sample, this implies we intend to go for a smaller confidence level c, or in terms of type I error, we look for higher value of alpha.
hence if we increase the value of alpha , the sample size will surely increase
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