W6 Set 1: Vocabulary & Rules

Parameter

A number that describes a population

Population mean μ

The mean of the entire population

Sample mean x̄

The mean of a sample

Population proportion p

The proportion of the population with a characteristic

Sample proportion p̂

The proportion of the sample with a characteristic

Population standard deviation σ

The standard deviation of the population

Sample standard deviation s

The standard deviation of the sample

Sample size n

The number of observations in the sample

Point estimate

A sample statistic used to estimate a population parameter

Confidence interval

A range used to estimate a population parameter

Confidence level

The percentage of confidence used for an interval

Critical value

A cutoff value used for an interval or hypothesis test

Standard error

The estimated standard deviation of a sampling distribution

Margin of error

The amount added and subtracted from a point estimate

Point estimate for μ

x̄

Point estimate for p

p̂

When to use Z for a mean

Use Z when σ is known

When to use t for a mean

Use t when σ is unknown and s is used

Degrees of freedom

n − 1 for a one mean t procedure

Z formula for a mean

z = (x̄ − μ) / (σ / √n)

t formula for a mean

t = (x̄ − μ) / (s / √n)

Confidence interval for μ using Z

x̄ ± z × σ / √n

Confidence interval for μ using t

x̄ ± t × s / √n

Confidence interval for p

p̂ ± z × √[p̂(1 − p̂) / n]

Margin of error formula

Critical value × standard error

Lower confidence limit

Point estimate − margin of error

Upper confidence limit

Point estimate + margin of error

Higher confidence level

Produces a wider interval

Larger sample size

Produces a narrower interval

Center of a confidence interval for μ

x̄

Center of a confidence interval for p

p̂

Meaning of a 95 percent confidence interval

About 95 percent of intervals from repeated samples contain the true parameter

95 percent confidence interval misconception

It does not mean there is a 95 percent probability the parameter is in this calculated interval

Confidence interval and individual values

A confidence interval does not give the percentage of individual observations inside it

Confidence interval claim inside

The interval does not contradict the claim

Confidence interval claim outside

The interval contradicts the claim

Null hypothesis H₀

The hypothesis containing the claimed equality

Alternative hypothesis H₁

The hypothesis representing the claim being tested

Level of significance α

The cutoff used to decide whether evidence is strong enough

p-value

The probability of getting a result at least as extreme when H₀ is true

Rejection region

Values of the test statistic that cause H₀ to be rejected

Reject H₀

There is enough evidence against H₀

Do not reject H₀

There is not enough evidence against H₀

Left tailed test

H₁ uses <

Right tailed test

H₁ uses >

Two tailed test

H₁ uses ≠

Less than

H₁ uses <

Greater than

H₁ uses >

Different from or changed

H₁ uses ≠

Equal claim

The equality goes in H₀

p-value decision rule

Reject H₀ when p-value ≤ α

Critical value decision rule

Reject H₀ when the test statistic is in the rejection region

Two tailed significance level

α is split between both tails

Right tailed p-value

Area to the right of the test statistic

Left tailed p-value

Area to the left of the test statistic

Two tailed p-value

Combined area in both tails

90 percent Z critical value

1.645

95 percent Z critical value

1.960

99 percent Z critical value

2.576

Type I error

Reject H₀ when H₀ is actually true

Type II error

Do not reject H₀ when H₀ is actually false

Sample size

The minimum number of observations needed for the desired precision

Margin of error and sample size

A smaller margin of error requires a larger sample

Confidence level and sample size

A higher confidence level requires a larger sample

Population variance σ²

The variance of the entire population

Variance hypothesis test

A test of a claim about the population variance