Different types of encoding affect a person’s ability to remember words. You can test this by asking a participant to first do a task involving either visual, auditory, or semantic encoding. Then ask the participant to recognize the encoded words. For example, for visual encoding, the participant may be asked to judge whether the word appears in all capital letters, whereas for auditory encoding, the participant may be asked to judge whether the word rhymes with another word.
A professor of cognitive psychology is interested in the percent accuracy on this memory encoding task among college students. She measures the percent accuracy for 64 randomly selected students. The professor knows that the distribution of scores is normal, but she does not know that the true average percent accuracy on this memory encoding task among college students is 0.794 percent correct with a standard deviation of 0.1110 percent correct.
The expected value of the mean of the 64 randomly selected students, M, is . (Hint: Use the population mean and/or standard deviation just given to calculate the expected value of M.)
The standard error of M is . (Hint: Use the population mean and/or standard deviation just given to calculate the standard error.)
The DataView tool that follows displays a data set consisting of 200 potential samples (each sample has 64 observations).
Data Set
Samples
Sample
Variables = 2
Observations = 200
Variables>
Observations>
Variable
Variable
Correlation
Correlation
Statistics for 200 Random Samples (n = 64) drawn from a normal distribution of Accuracy Scores
R was used to generate the samples.
Variable↓ Type↓ Form↓ Observations
Values↓ Missing↓
Sample Means Quantitative Numeric 200 0
Sample SD Quantitative Numeric 200 0
Suppose this professor happens to select Sample 83. (Hint: To see a particular sample, click the Observations button on the left-hand side of the DataView tool. The samples are numbered in the first column, and you can use the scroll bar on the right side to scroll to the sample you want.)
Use the DataView tool to find the mean and the standard deviation for Sample 83. The mean for Sample 83 is . The standard deviation for Sample 83 is .
Using the distribution of sample means, calculate the z-score corresponding to the mean of Sample 83. The z-score corresponding to the mean of Sample 83 is .
Use the Distributions tool that follows to determine the probability of obtaining a mean percent accuracy greater than the mean of Sample 83.
Standard Normal Distribution
Mean = 0.0
Standard Deviation = 1.0
-3
-2
-1
0
1
2
3
z
The probability of obtaining a sample mean greater than the mean of Sample 83 is .
If the sample you select for your statistical study is 1 of the 200 samples you drew in your repeated sampling, the worst-luck sample you could draw is . (Hint: The worst-luck sample is the sample whose mean is farthest from the true mean. You may find it helpful to sort the sample means: In Observations view click the arrow below the column heading Sample Means.)
