Psych Stats Quiz #3 4/17/23

Question 1

probability

Answer 1

statistical inference asserts probability that a particular assertation is true
always state conclusions in terms of probability not proof

Question 2

probability vs relative frequency

Answer 2

future vs past tense
relative frequency is used to express probability

Question 3

probability ex

Answer 3

cards - the probability of picking a red card from a deck of randomly shuffled cards = 1/2 or 50%
a spade = 1/4 or 25%

Question 4

random sampling with replacement

Answer 4

after picking an observation you put it back into the pool because if you don’t then the scores are considered independent
Ex. if cards are not replaced the probability changes on subsequent samples

Question 5

distribution of sample means

Answer 5

establish a set of rules that allows us to make inferences from a sample about the population
- this distribution is the answer to why we can generalize about population based on samples

Question 6

sampling distribution

Answer 6

a distribution of statistics obtained by selecting all samples of a specific size from the population (usually mean)

Question 7

mean sampling distribution

Answer 7

a collection of sample means for all possible random samples of a particular size that can be obtained from a particular population

Question 8

sample mean characteristics

Answer 8

cluster around the population mean
distribution is normal (central limit theorem)
can use distribution to answer probability questions

Question 9

the expected value of M

Answer 9

the mean of the distribution of sample means which is equal to the population

Question 10

standard error of sample means

Answer 10

the standard deviation of the distribution of sample means
standard deviation/square root of sample size
σ/√n

Question 11

standard error characteristics

Answer 11

standard or typical distance from the mean
specifies precisely how well a sample mean estimates the population

Question 12

hypothesis testing - z test steps

Answer 12

1) state hypothesis about an unknown population mean
2) set criteria for decision between hypotheses
3) collect sample data
4) evaluate null hypothesis

Question 13

criterion - alpha level

Answer 13

called the level of significance
probability value that is used to define “very unlikely”
p < 0.05

Question 14

single sample z test: directional

Answer 14

directional - upper and lower 2 1/2 % of normal distribution = -1.96 and 1.96

Question 15

single sample z test: one-tailed test

Answer 15

1.64, 0.05 = rejection region

Question 16

reject the null

Answer 16

when same data is substantially different from what the null predicts

Question 17

fail to reject the null

Answer 17

no evidence was found that the null is wrong, but can never be 100%

Question 18

type 1 error

Answer 18

null reject when treatment really does not have an effect
false positive

Question 19

type 2 error

Answer 19

null not reject when treatment does really have an effect
false negative

Question 20

infant affection holding example

Answer 20

μ = 26 pounds, n = 16, σ = 4
H₀: μinfants held = 26 pounds
H₁ = μinfants held≠ 26 pounds

standard error of mean (σm) = σ/√n = 4/√16 = 1

critical region test:
X = μH₀ (+/-)Z (σm)
X = 26 + 1.96(1) = 27.96
X = 26 - 1.96(1) = 24.04
24.04 ≥ X ≥ 27.96

fail to reject the null because 26 falls in the critical region, meaning that there is no effect on holding infants and their weight

Question 21

critical region test

Answer 21

X = μH₀ (+/-)Z (σm)

Question 22

z score

Answer 22

Z(i) = (X - μ)/σ(m)

Question 23

statistically significant

Answer 23

the null hypothesis was rejected

Question 24

p-value

Answer 24

the smallest critical region that would allow rejection of the null hypothesis - 0.05

Question 25

making 0.05 smaller

Answer 25

the rejection region moves out farther

Question 25

making 0.05 smaller

Answer 25

the rejection region moves out farther