Set 2 W6: Word Problems & Examples

Mean is claimed to be greater than a value

H₀: μ = value and H₁: μ > value

Mean is claimed to be less than a value

H₀: μ = value and H₁: μ < value

Mean is claimed to be different from a value

H₀: μ = value, H₁: μ ≠ value

Mean is claimed to have changed

H₀: μ = value and H₁: μ ≠ value

Mean claim is greater than the stated value

Right tailed test

Mean claim is less than the stated value

Left tailed test

Mean claim is different from the stated value

Two tailed test

Population σ is known

Use a Z procedure

Population σ is unknown and sample s is given

Use a t procedure

Sample mean with known σ

Use z = (x̄ − μ) / (σ / √n)

Sample mean with unknown σ

Use t = (x̄ − μ) / (s / √n)

Sample size for a mean

Use the given σ confidence level and desired margin of error to solve for n

Minimum sample size

Round the answer up to the next whole number

Confidence interval for μ with known σ

x̄ ± z × σ / √n

Confidence interval for μ with unknown σ

x̄ ± t × s / √n

Confidence interval for a proportion

p̂ ± z × √[p̂(1 − p̂) / n]

Sample has 27 successes out of 45

p̂ = 27 / 45 = 0.60

Sample has 14 successes out of 35

p̂ = 14 / 35 = 0.40

Sample has 78 successes out of 150

p̂ = 78 / 150

Sample mean is 53 Point estimate for μ?

= 53

Sample proportion is 0.38 Point estimate for p?

= 0.38

90 percent confidence interval what is z?

Use z = 1.645

95 percent confidence interval what is z?

Use z = 1.960

99 percent confidence interval what is z?

Use z = 2.576

Claim is inside the confidence interval

The interval does not contradict the claim

Claim is outside the confidence interval

The interval contradicts the claim

Confidence level increases

The confidence interval gets wider

Sample size increases

The confidence interval gets narrower

Margin of error decreases

A larger sample is needed

p-value is less than α

Reject H₀

p-value equals α

Reject H₀

p-value is greater than α

Do not reject H₀

Test statistic is in the rejection region

Reject H₀

Test statistic is outside the rejection region

Do not reject H₀

Right tailed test with α = 0.05 put what in what tail?

Put 0.05 in the right tail

Left tailed test with α = 0.05 put what in what tail?

Put 0.05 in the left tail

Two tailed test with α = 0.10 put what in what tail?

Put 0.05 in each tail

Right tailed p-value find the area to the X of the test statistic?

Find the area to the right of the test statistic

Left tailed p-value find the area to the X of the test statistic?

Find the area to the left of the test statistic

Two tailed p-value find the x area?

Find the combined area in both tails

Orange pH claim of 4.4 with sample x̄ = 4.2 and s = 0.5 : use what tail test?

Use a two tailed t test

Supercharger claim of 14.1 with sample x̄ = 14.8 and s = 1.7 : use what tail test?

Use a right tailed t test

Bulb lifetime claim of 51 months with known σ: use a ? test

Use a Z test when testing the mean

Player rating claim above 80: use a ? tailed test

Use a right tailed test

Confidence interval contains a medical group's claimed mean the claim is?…

not contradicted

Confidence interval does not contain a claimed mean the claim is?…

contradicted

Type I error after rejecting H₀

H₀ was actually true

Type II error after not rejecting H₀

H₀ was actually false

Population variance is being tested: parameter = ?

σ²

Variance is claimed to equal a value: H0 is?

H₀: σ² = value

Variance is claimed to differ from a value H0 is?

H₁: σ² ≠ value