PSYC 2317

Mark W. Tengler, M.S.

Assignment #8

Sampling Error

8.1For each of the following, assume that the sample was selected from a population with

= 70 and = 15.

a.What do you expect the value of M to be in a perfect world with no sampling error, if

you have a sample of n = 4 scores?

b.What is the standard error of M for a sample of n = 4 scores?

c.What do you expect the value of M to be in a perfect world with no sampling error, if

you have a sample of n = 25 scores?

d.What is the standard error of M for a sample of n = 25 scores?A

8.2population has a mean of = 65 and a standard deviation of = 10.

a.If you select a random sample of n = 4 scores from this population, how much error

would you expect between the sample mean and the population mean?

b.If you select a random sample of n = 25 scores from this population, how much error

would you expect between the sample mean and the population mean?

c.How much error would you expect for a sample of n = 100 scores?

8.3Welsch, Davis, Burke, and Williams (2002) conducted a study to evaluate the

effectiveness of a carbohydrate-electrolyte drink on sports performance and endurance.Experienced

athletes were given either a carbohydrate-electrolyte drink or a placebo while they were tested on

a series of high-intensity exercises. One measure was how much time it took for the athletes to run

to fatigue.Data similar to the results obtained in the study are shown in the following table:

Time to run to fatigue (in minutes)

GroupMeanSE

(standard error)

Placebo21.72.2

Carbohydrate-electrolyte28.62.7

a.Construct a bar graph that incorporates all of the information in the table.

b.Looking at your graph, do you think that the carbohydrate-electrolyte drink helps

performance?

Formula for Standard Error

Standard error measures the average amount of sampling error that can be expected to occur just by

chance through probability sampling methods.In other words, how much can we expect the sample

mean to vary above and below the mean most of the time through the sampling process.It is not a

measure of the total sampling error, but a measure of how much on an average we can expect the mean

to move due to sampling error.