Set 1 — Core Vocab and Rules

Density curve

Curve where total area equals 1

Density curve conditions

Curve stays at or above 0 and total area equals 1

Area under a density curve

Probability

Normal distribution

Symmetric bell shaped distribution

Normal distribution center

Mean equals median equals mode

Normal distribution spread

Standard deviation

Standard normal distribution

Normal distribution with mean 0 and standard deviation 1

Z score

Number of standard deviations a value is from the mean

Z score formula

z equals x minus mean divided by standard deviation

Positive z score

Value is above the mean

Negative z score

Value is below the mean

Z score of 0

Value equals the mean

Area under normal curve

Probability

Left tail area

Probability below a value

Right tail area

Probability above a value

Between area

Probability between two values

Table A.2

Table used to find normal areas and z scores

Normal proportion

Area under the normal curve

TI 84 normalcdf

Finds normal proportions

TI 84 invNorm

Finds a value from a proportion

Population

Entire group being studied

Sample

Smaller group taken from a population

Sample mean

Mean of a sample

Sampling distribution

Distribution of a statistic from repeated samples

Sampling distribution of x bar

Distribution of sample means

Mean of x bar

Population mean

Standard error of x bar

Population standard deviation divided by square root of n

Central Limit Theorem

Sample means become approximately normal for large samples

X bar z score

X bar minus population mean divided by standard error

Nth percentile

Value with n percent below it

Unusual x bar

Sample mean with a very small probability

Confidence interval

Range of plausible values for a population parameter

Confidence level

Long run percentage of intervals that capture the population parameter

Confidence interval form

Statistic plus or minus margin of error

Margin of error

Amount added and subtracted from the sample statistic

Higher confidence level

Wider confidence interval

Larger sample size

Smaller margin of error

Known population standard deviation

Use the z distribution

Unknown population standard deviation

Use the t distribution

Student t distribution

Symmetric distribution used when population standard deviation is unknown

Degrees of freedom

Sample size minus 1

T distribution versus normal

T distribution has heavier tails

Known sigma confidence interval

X bar plus or minus z star times sigma divided by square root of n

Unknown sigma confidence interval

X bar plus or minus t star times s divided by square root of n

Margin of error for mean

Critical value times standard error

Confidence interval width

Twice the margin of error

Sample proportion

P hat equals successes divided by n

Standard deviation of p hat

Square root of p times 1 minus p divided by n

Large population proportion interval

P hat plus or minus z star times square root of p hat times 1 minus p hat divided by n

Plus 4 confidence interval

Confidence interval using adjusted sample proportions

Plus 4 adjusted successes

Successes plus 2

Plus 4 adjusted failures

Failures plus 2

Plus 4 adjusted sample size

Original sample size plus 4

Adjusted sample proportion

Adjusted successes divided by adjusted sample size

Sample size for confidence interval

Number of observations needed for a desired interval width

Sample size for margin of error

Number of observations needed for a desired margin of error

Hypothesis test

Procedure used to evaluate a claim about a population

Null hypothesis

Statement of no change or no difference

Alternative hypothesis

Statement representing the claim being tested

Null hypothesis symbol

H sub 0

Alternative hypothesis symbol

H sub a

P value

Probability of a result at least as extreme assuming H sub 0 is true

Significance level

Alpha

Small P value

Strong evidence against H sub 0

P value less than alpha

Reject H sub 0

P value greater than alpha

Fail to reject H sub 0

Test statistic

Standardized value measuring distance from the null value

Known standard deviation hypothesis test

Use the P value method

Unknown standard deviation hypothesis test

Use the critical value method

Critical region

Values that lead to rejection of H sub 0

Statistically significant

Result is unlikely under H sub 0

Practically significant

Result has a meaningful real world effect

Statistical versus practical significance

Statistical asks whether an effect is unlikely while practical asks whether it matters