Question

Suppose that Body Mass Index (BMI) for a population of 30-60-year-old men follows a Normal distribution with mean 26, and standard deviation 4. Q: Please calculate the range of BMI that 95% of subjects fall within:

Suppose we know that the prevalence of asthma among American children is 11%. Researchers conducted a study among 600 children in Boston and found that 56 had asthma. Q:Suppose researchers originally planed to enroll 1000 children, but they had to reduce the sample size to 600 due to budget deficit. Which of the following decreased compared to the original design? A. The power of the hypothesis test B. The probability of making a Type I error C. The probability of making a Type II error D. The sample mean

Answer 1

Solution1 ) Suppose that Body Mass Index (BMI) for a population of 30-60-year-old men follows a Normal distribution with mean 26, and standard deviation is 4.

the range of BMI that 95% of subjects fall within:

the range of BMI that 95% of subjects fall within:

If we use 1.96 instead of 2 then our 95% confidence interval is

This is 95% confidence interval

SOLUTION 2) p= 0.11 , n=600 and x= 56

p(hat)= 56/600= 0.093

q(hat)= 1-0.093= 0.907

Z= p-p(hat)/sqrt(p(hat)*q(hat)/n)

Z= 0.11-0.093/sqrt(0.093*0.907/600)

Z= 0.017/0.290

Z= 1.434 for n=600

Z= 2.338 FOR n=1000

If we use n =1000 then The probability of making a Type II error gets DECREASED.