Topic 4 Assessment: Understanding Sample Variability & Sampling Distributions

Topic 4 Assessment: Understanding Sample Variability & Sampling Distributions

This assignment uses data from the 2014 version of the National Survey of Drug Use and Health conducted by SAMSHA – https://www.samhsa.gov/data/population-data-nsduh. In this assessment, you will be working with data the ALCOHOL subset.  Specifically, the ALCOHOL data set contains information on 40,125 individuals who answered “Yes” to the question of whether they had ever used alcohol.  The dataset is ALCOHOL.sav and posted in the Assignments folder.

 Question 1: Population Parameters

Use the Frequencies or Descriptive function in SPSS or PSPP to produce the Mean and Standard Deviation for the variable “ALCTRY”, which records the age in years when a survey respondent first used alcohol.

The mean and standard deviation for ALCTRY are based on all cases associated with alcohol use within this SPSS file only, which technically makes the mean and standard deviation sample data (statistics). The true population of those who have ever tried alcohol would be much larger than 40,125.  However, for purposes of this exercise, the mean and standard deviation for ALCTRY will be considered (are being used as) the population parameters  – the population mean and population standard deviation.

• Level of measurement for ALCTRY: Scale

• Population MEAN (when first tried alcohol)

• Population Standard Deviation (for the ALCTRY variable)

• Calculate the age range that would be between Z = -1 and Z = +1

The Age range between Z- -1 and Z=+1 would be

• Calculate the age range that would be between Z = -2 and Z = +2

This last range would be the range of normal first use of alcohol for the population.

Also, you might want to look at the histogram ….  

Question 2: Examining sample variability through samples of n = 50.

SPSS and PSPP allow a user to select random samples of various sizes.  Below I have listed the average age of first use (the sample mean) from four random samples from three sample sizes; four random samples of size n = 50, four random samples for n = 100 and four random samples for n = 300.  Calculate the standard errors and Z scores for all samples.  Round your standard errors and Z scores to two decimal places. 

Sampling Distribution of Samples of n = 50

Shape =                                  Mean =                                   Standard Error =