PS 201 Sampling Lab
The purpose of this lab is to explore the relationship between a sample distribution and a sampling distribution. You should write all samples down on the answer sheet and turn in all work before leaving lab today.
1. Draw a sample of size 20 and calculate the mean, median, mode, range, variance, and standard deviation.
a. Report your mean and standard deviation to the lab assistant.
b. Do a frequency distribution, a grouped frequency distribution (start at 10, with a CI of 3, 10-12,13-14 etc.) and draw a histogram of the data (next page). Is the data normally distributed?
2. Given that the m= 28 and s= 5
a. What is the probability that on one trial you draw a number which is 22 or less.
b. What is the probability that you draw a number between 27 and 29 (inclusive).
c. What is the percentile rank of a score of 32. What about 18?
3. Draw 5 samples of size 5 and 5 samples of size 15.
a. Calculate the mean and standard deviation for each sample.
b. Why do the means differ from each other?
c. Calculate the grand mean and standard deviation of the grand mean for the n=5 and n=15 samples.
d. What do you notice about the differences between the grand means and their standard deviations? Why would it be that way?
4. Calculate the standard error of the mean (using sigma) for n = 15.
a. Compare that value to the standard deviation of the grand means. Would you expect them to be similar? Why/Why not?
b. Using mu = 28.00 and sigma=5.00, what is the probability of drawing a sample of n=15 with a mean of 30 or greater.
5. Using your original sample of size 20.
a. Test the null hypothesis that the true mean of this population is 28. Use known sigma 5.00 by:
state null and alternative hypothesis symbolically (two tailed)
test at alpha = .05
what is the decision rule
what is the decision.
6. Draw a paired sample of size 10.
a. pick one set to be x and the other to be y.
b. draw a scatter plot (next page).
c. calculate r and the slope (b) and intercept (a).
d. calculate any two points and draw the line
e. what is the predicted y score for an x score of 22 and 28.
d. what correlation would you expect to get on average if you repeated this process of drawing paired numbers many times (Explain)
Main Sample (n=20) / Samples (n=5)Grand Mean and St. dev
Mean =
St. dev =
Samples (n=15)
Mean=
St. dev=
Grand Mean and St. dev
Mean =
St. dev =
Plot Grouped Histogram Data Here:
X / Y
Mean =
St. dev =
Plot Scatterplot and Regression Here: