Equations
√[ ∑(x - x̄)2/ N ]
Standard Deviation for Population
What requires that each individual in the population has an equal chance of being selected?
With μ=87 and σ=12, what is the probability a sample of n=49 would have an average score between x̄ = 83 and x̄ = 89?
86.94%
What are the two types of hypotheses?
Null and alternative.
Calculate the mean for the following:
6, 8, 6, 2, 10, 12, 4, 4, 7, 3
6.2
σ /√n
Standard Error
What occurs when a researcher fails to reject a null hypothesis that is really false?
Type II error
With μ=50 and σ=8, what is the probability of randomly selecting an individual with a score greater than X=56?
22.66%
A psychology lab uses rats to do experiments in the areas of learning and animal behavior. The supervisor of the lab suspects the company who supplies rats to the lab is not being honest. The company claims the boxes of rats it ships to the lab contain an average of μ=40 and σ=2 rats. The lab supervisor suspects the lab is receiving significantly fewer rats than the company is claiming. To test her suspicions, what type of test would she conduct?
One-tailed test
Draw and label on the board the Normal Curve Distribution with the corresponding percentages for standard deviations of 1, 2, and 3.
Percentages are 68%, 95%, 98%
(x - μ)/σ
Population Z-score
For any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will have a mean of μ and a standard deviation of σ / √ n
Central Limit Theorem
With μ=50 and σ=8, what is the probability of randomly selecting an individual with a score lower than X=62?
93.32%
Historically, evening long-distance calls have averaged 15.2 minutes per call. A study of a random sample of 35 long-distance calls in 2010 revealed a mean time of 16.1 minutes. Assume the standard deviation is known to be 5 minutes. Using a .05 level of significance, is there sufficient evidence to conclude the average evening long-distance call time has increased?
There is insufficient evidence to conclude that the average evening long-distance call time has increased, with .05 level of significance.
What refers to the probability value that is used to define the concept of “very unlikely”?
Alpha Level
(Number of events A)/(All possible events)
Probability
What occurs when a researcher incorrectly rejects the null hypothesis? This can also cause a "false positive" result.
Type I error
With μ=87 and σ=12, what is the probability a sample of n=25 would have an average score greater than x̄ = 90?
10.56%
Suppose an editor of a publishing company claims that the mean time to write a textbook is less than 15 months. A sample of 16 textbook authors is randomly selected and it is found that the mean time taken by them to write a textbook was 12.5 months. Assume that the standard deviation is known to be 3.6 months. Using a .05 level of significance, is the editor correct in his claim that it takes less than 15 months to write a textbook?
There is sufficient evidence to conclude the editor's claim is true, with .05 level of significance.
Calculate the standard deviation for the following sample:
9,10,11,7,13
2.236
( Σx ) / n
Sample mean
What specifies the precise location of each X value within a distribution and standardizes the values to put them on the same scale?
Z-score
With μ=50 and σ=8, what is the percentile rank for a score of X=59?
47.52
A researcher who studied hair loss in men believed there was a link between the age at which men lose their hair and whether or not they smoked. In the general population, males typically begin losing their hair at an average age of μ=48 and σ=4 years. The researcher collected sample of n = 13 with x̄ = 48.31. Using an alpha level = .01, can the researcher conclude that males who smoke on a regular basis begin to lose their hair at an age that is significantly different than males in the general population?
Fail to reject null hypothesis. There is no significant difference.
Z-scores are an example of what kind of statistic?
Inferential Statistic