Hypothesis Testing Statistics Introduction

Define a Type I error?

• The failure to reject a false null hypothesis
• Rejecting a true null hypothesis
• The acceptance to reject a null hypothesis
• Accepting a true null  hypothesis

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

• H₀: μ > 64"

  Hₐ: μ ≠ 64"

• H₀: μ < 64"

  Hₐ: μ > 64"

• H₀: p > 64"

  Hₐ: p ≠ 64"

• H₀: p = 64"

  Hₐ: p > 64"

The weight of the average 6th grade student's backpack (with books in it) is 18.4 lbs. The principal of the school thinks that the backpack does not weight 18.4 lbs. What is the null and alternate hypothesis?

• H0: $$\mu$$ = 18.4
  Ha: μ = 18.4

• H0: μ = 18.4
  Ha: μ > 18.4

• H0: μ = 18.4
  Ha: μ < 18.4

• H0: μ = 18.4
  Ha: μ ≠ 18.4

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 17, 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 = 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 : μ = 47

  H_a : μ = 47

• H₀ : μ = 47

  H_a : μ < 47

• H₀ : μ = 47

  H_a : μ > 47

• H₀ : μ = 47

  H_a : μ ≠ 47

In a hypothesis test, the alternative hypothesis is always a statement of equality. 

• True
• False

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