Exam 2 (Chapters 5-8)

Question 1

binomial data

Answer 1

two (bi) names (nominal) data that can take on just two possible values.
ex: correct/incorrect, left/right, heads/tails.
treat the two possible values as events.

Question 2

probability

Answer 2

random sampling = random sampling w/replacement each time an individual is selected, they are placed back into the population. this means that the probability of selecting any specific individual remains constant as you collect the sample

Question 3

proportions of the normal distribution

Answer 3

the normal distribution’s shape is exactly known, so the proportion of scores between any two values can be determined. The proportion and the probability mean the same thing.

Question 4

standard error of the mean and bar charts

Answer 4

the standard error of the mean tells you about how much variability in a sample size of N can be expected due to “sampling error” (the idea that, because individuals are randomly selected for the sample, the mean score will vary depending upon who happens to be picked for the sample). larger samples have smaller error, because SEM = σ/√N.

Question 5

null hypothesis testing

Answer 5

Type I error refers to the possibility of “false positives”—a result is called significant that actually occurred due to random chance (sampling error). the likelihood of Type I error is the same as alpha, the criterion for deciding what counts as “significant”. if alpha = 0.05, two-tailed, then there is a 5% chance total of a Type I error.

Question 6

null hypothesis - significance

Answer 6

• a significant result has probability LESS THAN alpha, which means that the Z-score for the sample mean is more extreme than the critical Z-score (the Z-score that matches alpha…for example, alpha = 0.05 two tailed has critical Z of +- 1.96).
• a result that is NOT significant has probability GREATER THAN alpha, which means the Z-score for the sample mean is less extreme (closer to zero) compared to the critical Z-score.
• concluding that a result is not significant means failing to reject the null hypothesis—the decision is that the probability that the result is due to random chance (sampling error) was too high (“maybe the result was just a fluke”). If you conclude “not significant” but actually the result its real, this is a Type II error: a “false negative”.

Question 7

note about statistical power

Answer 7

you want high statistical power—this means the statistical test (like the Z-score) will probably lead you to conclude that there is a significant effect if there really is one.

Question 8

Z-scores: raw scores vs. sample means

Answer 8

when you need to know the probability of a single raw score, you use Z = (X-μ)/σ, but when you need to know about the mean of a sample, you must take into account the sample size. so in that case, use Z = (M-μ)/SEM, where SEM=σ/√N.
in any situation, you can use Z = (M-μ)/SEM, because if you have only one score, then M and X are the same thing, and N = 1 (which means SEM = σ/√1 which is just σ).

Question 9

Z-scores & binomial data

Answer 9

if the data are binomial then two things change for finding the Z-score. - - - the stdev is s = √(npq), where n is the number of data points (called “trials”), p = the probability of the event you are interested in (e.g., heads, correct, etc.) and q = the probability of the other event (e.g., tails, incorrect, etc.).
- second, when doing Z = (X-M)/s, the value of X must use the “real intervals”, so if you are interested in for example flipping a heads 15 times, you will use either 14.5 or 15.5. if you want to find the odds of flipping “15 or more”, you would use 14.5 and up (because that will include 15). if you are interested in “more than 15”, that means not including 15, and so you would use 15.5 and up.