Hypothesis Testing

Which of the following is the definition of 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 65"

• H₀: μ > 65"

  Hₐ: μ ≠ 65"

• H₀: μ < 65"

  Hₐ: μ > 65"

• H₀: p > 65"

  Hₐ: p ≠ 65"

• H₀: p = 65"

  Hₐ: p > 65"

A researcher claims that the mean cost of a dozen eggs is greater than $5. Suppose the P-value for an associated hypothesis test is 0.0304. Using a = 0.05, what is the properly constructed conclusion?

• There is sufficient evidence to reject the claim that the population mean cost of a dozen eggs is $5 at the 0.05 significance level. Therefore, we can support researcher's claim.

• There is insufficient evidence to reject the claim that the population mean cost of a dozen eggs is $5 at the 0.05 significance level. Therefore, we can support researcher's claim.

• There is sufficient evidence to reject the claim that the population mean cost of a dozen eggs is more than $5 at the 0.05 significance level. Therefore, we can support researcher's claim.

• There is sufficient evidence to reject the claim that the population mean cost of a dozen eggs is more than $5 at the 0.05 significance level. Therefore, we cannot support researcher's claim.

When the p-value is greater than alpha we:

• Reject Ho

• Fail to reject Ha

• Fail to reject Ho

• Reject Ha

Of the following, which is the only appropriate option for the null hypothesis? 

• H₀: p = k

• H₀: μ > k

• H₀: μ < k

• H₀: p ≠ k

Of the following, which is not an appropriate option for an alternate hypothesis? 

• H_a: μ = k

• H_a: μ > k

• H_a: p < k

• H_a: μ ≠ k

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: μ = 18.4

  H_a: μ = 18.4

• H₀: μ = 18.4

  H_a: μ > 18.4

• H₀: μ = 18.4

  H_a: μ < 18.4

• H₀: μ = 18.4

  H_a: μ ≠ 18.4

When must you use a t-test instead of a z-test? 

• When the population standard deviation is known.

• When the sample standard deviation is known.

• When the sample standard deviation is unknown.

• When the population standard deviation is unknown.

Tags

CCSS.HSS.ID.A.4

A test is made of H₀ : µ = 17 versus H_a : 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 actually 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 H_a : 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 actually 10, is the conclusion a Type I Error, Type II error, or a correct decision?

• Type I

• Type II

• Correct Decision