Main Vocab

Question 1

when describing a distribution of data, mention..

Answer 1

1. shape
2. center
3. variability (spread)
4. unusual features (outliers or gaps)
   Always include context!

Question 2

A five-number summary includes..

Answer 2

Minimum, Q1, median, Q3, maximum

Question 3

a z-score tells us..

Answer 3

The number of standard deviations above or below the mean.

Question 4

the empirical rule

Answer 4

in a normal distribution:
about 68% of the values lie within 1 standard deviation of the mean
about 95% of the values lie within 2 standard deviations of the mean
about 99.7% of the values lie within 3 standard deviations of the mean

Question 5

when describing a bivariate distribution (scatterplot), mention..

Answer 5

1. direction (positive or negative)
2. strength (strong or weak)
3. form (linear or non-linear)
4. unusual features
   Always include context!

Question 6

residual

Answer 6

Observed value - predicted value. y − ŷ

Question 7

When asked to interpret the slope of a regression line in context, say..

Answer 7

“On average, there is a predicted [increase or decrease] of [slope][units] in [the dependent variable] for every
increase of one [unit] in [the independent variable].”

Question 8

When asked to interpret the y-intercept of a regression line in context, say..

Answer 8

“On average, when the value of [the independent variable] is zero [units], [the dependent variable] is predicted
to be [y-intercept] [units].”

Question 9

When asked to interpret the coefficient of determination of a regression line, r2, in context, say..

Answer 9

“[r^2] percent of the variation in [the dependent variable] can be explained by the linear relationship between
[the dependent variable] and [the independent variable].”

Question 10

When writing about bias in sampling methods..

Answer 10

1. Identify the population and sample.
2. Explain how the sampled individuals differ from the general population
3. Explain how this leads to an overestimate or underestimate

Question 11

Two events A and B are independent if

Answer 11

P(A|B) = P(A) and P(B|A) = P(B)

Question 12

Two events A and B are mutually exclusive if

Answer 12

P(A ∩ B) = 0

Question 13

The probability of the union of two events A and B can be found by

Answer 13

P(A ∪ B) = P(A) + P(B) − P(A ∩ B)

Question 14

The probability of the intersection or “joint probability” of two events A and B can be found by

Answer 14

P(A ∩ B) = P(A) ∙ P(B|A)

Question 15

Conditions for a one-sample z interval for a population proportion

Answer 15

1. the data are collected using a random sample
2. when sampling without replacement, the sample size is less than 10% of the population
3. np̂≥ 10 and n(1 − p̂) ≥ 10

Question 16

Margin of error

Answer 16

(critical value)(standard error)

Question 17

When asked to interpret a confidence interval, say..

Answer 17

“We are [confidence level] confident that the interval from ___ to ___ captures the true [parameter in context].”

Question 18

When asked to interpret a confidence level, say..

Answer 18

“If we take random samples of size [n] from the population of [population in context] and use each sample to construct a
[confidence level] confidence interval, about[confidence level] of those intervals would capture the true
[parameter in context].”

Question 19

Conditions for a one-sample z test for a population proportion

Answer 19

1. the data are collected using a random sample
2. when sampling without replacement, the sample size is less than 10% of the population
3. np0 ≥ 10 and n(1 − p0) ≥ 10

Question 20

When concluding a hypothesis test, say..

Answer 20

Because the p-value of ____ ≤ α = _____ , we reject H0. There is convincing statistical evidence that [Ha in context]
OR
Because the p-value of ____ ≥ α = _____ , we fail to reject H0. There is not convincing statistical evidence that
[Ha in context]

Question 21

Conditions for a two-sample z interval for a difference in population proportions

Answer 21

1. the data are collected using random samples or random assignment to treatment groups
2. when sampling without replacement, the sample sizes are both less than 10% of the population
3. n1p̂1 ≥ 10
   n1 (1 − p̂1) ≥ 10
   n2p̂2 ≥ 10
   n2 (1 − p̂2) ≥ 10

Question 22

power

Answer 22

the probability of not making a Type II error

Question 23

Conditions for a two-sample z test for a difference in population proportions

Answer 23

1. the data are collected using random samples or random assignment to treatment groups
2. when sampling without replacement, the sample sizes are both less than 10% of the population
3. n1 (pc) ≥ 10
   n1(1 − pc) ≥ 10
   n2(pc) ≥ 10
   n2(1 − pc) ≥ 10

Question 24

Conditions for inferencing with a population mean

Answer 24

1. the data are collected using random samples or random assignment to treatment groups
2. when sampling without replacement, the sample size is less than 10% of the population
3. n ≥ 30
   OR
   If n < 30, the sample data is free of skew or outliers

Question 25

Conditions for a two-sample t interval for a difference in population mean

Answer 25

1. the data are collected using random samples or random assignment to treatment groups
2. when sampling without replacement, the sample sizes are less than 10% of the population
3. n1 ≥ 30 and n2 ≥ 30
   OR
   If n < 30, the sample data is free of skew or outliers

Question 26

Conditions for a Chi-Square test

Answer 26

1. the data are collected using random samples or random assignment to treatment groups
2. all expected counts are greater than or equal to 5
3. trials are independent