An investigator wants to design a study to estimate the difference in the mean BMI between boys and girls age 12 living in new york city

An investigator wants to design a study to estimate the difference in the mean BMI between boys and girls age 12 living in new york city. How many boys and girls are needed to ensure that a 95{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} confidence interval estimate for the difference in mean BMI between boys and girls has a margin of error not exceeding 2 units? Use the estimate of the variability in BMI from Problem 7.
Problem 7 states. The Mean body mass index (BMI) for boys age 12 is 23.6. An investigator wants to test if the BMI is higher in boys age 12 living in New York City. How many boys are needed to ensure that a two- sided test of hypothesis has 80{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} power to detect an increase in BMI of 2 units? Assume that the standard deviation in BMI is 5.7.
AN INVESTIGATOR wants to design a study to estimate the difference in the proportion of men and women who develop early onset cardiovascular disease ( defined as cardiovascular disease before age 50). A study conducted 10 years ago found that 15{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} and 8{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} of men and women, respectively, developed early onset cardiovascular disease. How many men and women are needed to generate a 95{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} confidence interval estimate for the difference in proportions with a margin of error not exceeding 4{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119}?
A clinical trial was conducted comparing a new compound designed to improve wound healing in Trauma patients to a placebo. After treatment for 5 days, 58{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} of the Patients taking the new compound had a substantial reduction in the size of their wound as compared to 44{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} in the placebo group. The trial failed to show significance. How many subjects would be required power detect the difference in proportions observed in the trial with 80{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} power? A TWO- SIDED TEST is planned at a=0.05.
An investigator wants to estimate caffeine consumption in high school students, How many students would be required to ensure that a 95{0e601fc7fe3603dc36f9ca2f49ef4cd268b5950ef1bbcf1f795cc00e94cdd119} confidence interval estimate for the mean caffeine intake (measure in mg) is within 15 units of the true mean? Assume that the standard deviation in caffeine intake is 68 mg.