Use results of Exercises 8.75 to 8.78 and relevant findings from the Internet to make a report on children's fitness, weight, and TV-watching habits that relies on statistical information.
Exercises 75 to 78
Exercise 75
Children's gross motor development is assessed with an overall motor quotient, MQ, which was found to follow an approximate normal distribution for a large group of school children, with mean 93 and standard deviation 15.
a. What are the mean and standard deviation of sample mean MQ for a random sample of 144 children? b. What are the mean and standard deviation of sample mean MQ for a random sample of 36 children? c. In general, what values of sample mean MQ will result in a standardized sample mean (z) that is positive?
d. A sample of 144 children who participated in both club sports and regular sports had a mean MQ of 96.5. Report the z-score for this sample mean and use it to explain whether or not these children appear to be representative of the larger group in terms of MQ.
e. A sample of 36 obese children had a mean MQ of 85.7. Report the z-score for this sample mean and use it to explain whether or not these children appear to be representative of the larger group in terms of MQ.
Exercise 76
Children's gross motor development is assessed with an overall motor quotient, MQ, which was found to follow an approximate normal distribution for a large group of school children, with mean 93 and standard deviation 15.
a. What is the standard deviation of sample mean for samples of size 25?
b. Report the interval centered at the mean that has a 95% probability of containing the sample mean for random samples of size 25.
c. What is the probability that sample mean is less than 90 or greater than 96?
Exercise 77
Children's fitness is assessed by finding the distance, in meters, that they can run in 6 minutes. Overall, this distance varies fairly normally, with mean 835 and standard deviation 111.
a. What are the mean and standard deviation (to one decimal place) of sample mean distance run for a random sample of 289 children?
b. What are the mean and standard deviation (to one decimal place) of sample mean distance run for a random sample of 38 children?
c. In general, what values of sample mean fitness will result in a standardized sample mean (z) that is negative?
d. A sample of 289 children who watched TV daily ran a mean distance of 834.1 meters. Find the z-score for this sample mean.
e. Use the z-score from part (d) to explain whether or not these children appear to be representative of the larger group in terms of distance run.
f. A sample of 38 underweight children ran a mean distance of 838 meters. Find the z-score for this sample mean.
g. Based on your z-score, do these underweight children appear to be representative of the larger group in terms of distance run?
Exercise 78
Children's fitness is assessed by finding the distance, in meters, that they can run in 6 minutes. Overall, this distance varies fairly normally, with mean 835 and standard deviation 111.
a. What is the standard deviation of sample mean for samples of size 9?
b. Report the interval centered at the mean that has a 95% probability of containing sample mean for random samples of size 9.
c. What is the probability that sample mean is less than 761 or greater than 909?