Math Elementary Statistics Homework Help /Mathematics – Statistics
Lab 8A Simulating IQ Scores
This activity will involve simulating data to represent IQ scores. After generating large samples of IQ scores, you will construct a sampling distribution for the mean and find its mean and standard deviation. You will also compare proportions calculated from the sampling distributions to those predicted by the normal distribution.
1. a. Use StatCrunch to obtain 500 random samples of size n = 10 from the population of IQ
scores with a mean of 100 and a standard deviation of 15.
(Go to StatCrunch>Data>Simulate>Normal>Rows: 500 & Columns: 10>Normal parameters: Mean: 100 & Std. Dev.: 15)>Compute!
b. Compute the sample mean for each of the 500 samples. Provide the sample mean for
Sample 1 and Sample 2 here.
(Go to StatCrunch>Stat>Summary Stats>Select all columns using Shift Key>Statistics: Mean>Check Store in data table>Compute!
Mean from sample 1: ______________
Mean from sample 2:______________
2. a. What do you expect the mean and standard deviation of the sampling distribution of
the mean to be?
b. Draw a histogram of the 500 sample means. If possible, draw the theoretical normal
model on the histogram.
c. Determine the mean and standard deviation of the 500 sample means. Are these values
close to what was expected in part (a)?
d. What proportion of the 500 random samples resulted in a sample mean IQ greater than
108?
Based on the normal model, what proportion of random samples of size n = 10 would
we expect to result in a sample mean greater than 108?
Is the theoretical proportion obtained from the model close to the proportion from the
simulation? Explain.
Fundamentals of Statistics by Sullivan, III, 5e
