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A population consists of the 5 measurements 2, 6, 8, 0 and 1 and samples of size n = 2 . What is the variance of the population? 2 DECIMAL PLACES
. An investigator wants to compare two diet programs in children who are obese. One diet is a low-fat diet, and the other is a low carbohydrate diet. The plan is to enroll children and weigh them at the start of the study. Each child will then be randomly assigned to either the low fat or the low carbohydrate diet. Each child will follow the assigned diet for 8 weeks, at which time they will again be weighed. The number of pounds lost will be computed for each child. Based on data reported from diet trials in adults, the investigator expects that 20% of all children will not complete the study. A 95% confidence interval will be estimated to quantify the difference in weight loss between the two diets and the investigator would like the margin of error to be no more than 3 pounds. How many children should be recruited into the study?
An investigator wants to estimate the mean birth weight of infants born full term (approximately 40 weeks gestation) to mothers who are 19 years of age and under. The mean birth weight of infants born full-term to mothers 20 years of age and older is 3,510 grams with a standard deviation of 385 grams. How many women 19 years of age and under must be enrolled in the study to ensure that a 95% confidence interval estimate of the mean birth weight of their infants has a margin of error not exceeding 100 grams? Try to work through the calculation before you look at the answer.
. An investigator wants to estimate the mean systolic blood pressure in children with congenital heart disease who are between the ages of 3 and 5. How many children should be enrolled in the study? The investigator plans on using a 95% confidence interval (so Z=1.96) and wants a margin of error of 5 units. The standard deviation of systolic blood pressure is unknown, but the investigators conduct a literature search and find that the standard deviation of systolic blood pressures in children with other cardiac defects is between 15 and 20. To estimate the sample size, we consider the larger standard deviation in order to obtain the most conservative (largest) sample size.
. A normally distributed population has mean 57,800 and standard deviation 750.
a. Find the probability that a single randomly selected element X of the population is between 57,000 and 58,000.
b. Find the mean and standard deviation of 𝑥̅for samples of size 100.
c. Find the probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000.
A normally distributed population has mean 1,214 and standard deviation 122.
a. Find the probability that a single randomly selected element X of the population is between 1,100 and 1,300.
b. Find the mean and standard deviation of 𝑥̅for samples of size 25.
c. Find the probability that the mean of a sample of size 25 drawn from this population is between 1,100 and 1,300.
A normally distributed population has mean 57.7 and standard deviation 12.1.
a. Find the probability that a single randomly selected element X of the population is less than 45
b. Find the mean and standard deviation of 𝑥̅for samples of size 16.
c. Find the probability that the mean of a sample of size 16 drawn from this population is less than 45.
In the 2019 midterm election, a pollster was assigned to interview the oldest male and female in various households. Each was asked whether he or she voted for Vico Sotto. If the male said “Yes” and the female said “No,” the pollster recorded YN. Construct the probability distribution of the number of YES answers then find the mean, variance, and standard deviation.
Make a study about how many sheets of paper you consumed weekly in
answering your Self Learning Modules. Record the quantity (total number of sheets)
per subject, then construct a probability distribution. Compute the mean, variance,
and the standard deviation of the probability distribution you made. Interpret the
result, then find out how many weeks you will consume 50 sheets of pad paper.
Let the population be given by the numbers. Take all random samples of size 3 without replacement and obtain the sampling distribution of the sample mean
