Statistics Hypothesis

When do you use a t-value instead of a z-value?

• When n < 30

• When n ≥ 30

• When all of the planets align

• When the teacher says so

Which of the following is the FIRST step of a hypothesis test?

• Check assumptions & conditions

• Find your test statistic

• State your conclusion

• State your null & alternative hypotheses

A test is made of H₀ : µ = 17 versus H₁ : µ < 17 is performed using α = 0.01 significance level. The value of the test statistic is z = -2.68 and it is concluded that H₀ is rejected.

If the true value of µ is 10, is the conclusion a Type I Error, Type II error, or a correct decision?

• Type I

• Type II

• Correct Decision

A test is made of H₀ : µ = 50 versus H₁ : µ =/= 50 is performed using α = 0.01 significance level. The value of the test statistic is z = -2.68 and it is concluded that we fail to reject H₀ .

If the true value of µ is 65, is the conclusion a Type I Error, Type II error, or a correct decision?

• Type I

• Type II

• Correct Decision

A test is made of H₀ : µ = 50 versus H₁ : µ =/= 50 is performed using α = 0.01 significance level. The value of the test statistic is z = -2.68 and it is concluded that we fail to reject H₀ .

If the true value of µ is 50, is the conclusion a Type I Error, Type II error, or a correct decision?

• Type I

• Type II

• Correct Decision

A car manufacturer advertises that its new subcompact models get 47 mpg. If μ is the mileage of these cars, what could be the null and alternate hypothesis if we wanted to check if the car's mpg is overrated?

• H₀ = 47
  H_a = 47

• H₀ = 47
  H_a < 47

• H₀ = 47
  H_a > 47

• H₀ = 47
  H_a ≠ 47

At the Chrysler manufacturing plant, there is a part that is supposed to weigh precisely 19 pounds. The engineers take a sample of parts and want to know if they meet the weight specifications. What are our null and alternative hypotheses?

• H_o : μ = 17, H_a : μ ≠ 19

• H_o : μ = 19, H_a : μ ≠ 19

• H_o : μ = 19, H_a : μ ≠ 17

• H_o : μ = 17, H_a : μ ≠ 17

Use the notation to state the alternative hypothesis and null hypothesis: "Less than 4% of high school students take Statistics."

• H_o : X ≥ 4% and H₁ : X > 4%

• H_o : X ≤ 4% and H₁ : X < 4%

• H_o : X ≥ 4% and H₁ : X < 4%

• H_o : X > 4% and H₁ : X ≤ 4%

This symbol denotes the alternative hypothesis

• Null hypothesis

• Alternative hypothesis

• H₀

• H_a

Which of the following symbols can be in the NULL hypothesis? (Select ALL that apply)

• =

• >

• <