KNR 445
Statistical Applications in Science & Technology

Standard Error of the Mean

The purpose of this assignment is to demonstrate how the Standard Error of the Mean (SE_M) is calculated by hand and with SPSS, and how the SE_M is used to calculate confidence intervals for the population mean. The dataset to be used is the CDC smoking data.

Homework

1. Identify all the procedures in SPSS that can be used to calculate the standard error of the mean.

2. Using the data CDC data:
    a. Using random selection, draw 15 different samples of n = 12, using the variable of Tax per pack. 
        i. Calculate the mean of each of the 15 samples
        ii. Calculate the mean of the 15 sample means
        iii. Calculate the standard deviation of the 15 sample means
            (a) What is another name for the Standard Deviation just calculated?
        iv. Calculate the 95% and 99% Confidence Intervals for the Population Mean.
        v. Present the two confidence intervals in sentence format.
        vi. Do the Confidence Intervals calculated in iv contain the actual Population Mean?
SPSS Output for Question 2.

3. Create a histogram of the 15 sample means, and overlay the normal curve.
    a. What is another name for the distribution just plotted?
    b. Does the distribution resemble a normal curve?
    c. What will happen to the shape of the distribution if more sample means of the same size are calculated?
SPSS Output for Question 3.

4. For 2 of the different samples:
    a. Calculate
        i. the SEM for each of the two different samples.
        ii. the 68, 78 and 88% confidence intervals
        iii. the 95 and 99% confidence intervals, and express these in sentence format
SPSS Output for Question 4.