Week 14 Quiz

A field team weighed 151 Adelie penguins: x̄ = 3,700.66 g, s = 458.57 g, and SE = 37.32 g. A claim says the population mean μ is 4,000 g. What is the one-sample t statistic for testing H₀: μ = 4,000 g?

Select one.

• t ≈ −0.65
• t ≈ −299.34
• t ≈ −8.02
• t ≈ −1.32

The Palmer study recorded 44 Adelie penguins among 168 on Biscoe and 56 Adelie penguins among 124 on Dream. Which procedure tests whether the share of Adelie penguins differs between the two islands?

Select one.

• A one-sample t test
• A two-sample t test
• A one-proportion z test
• A two-proportion z test

Software compares mean body mass for 123 Gentoo and 151 Adelie penguins and reports: difference in means 1,375.35 g, standard error of the difference 58.81 g, Welch t = 23.386, about 249.6 degrees of freedom, and a p-value far below 0.001. Which reported number measures the gap in standard errors?

Select one.

• The difference, 1,375.35 g
• Welch t, 23.386
• The standard error, 58.81 g
• The degrees of freedom, 249.6

Two-sample software output for Gentoo versus Adelie body mass reports about 249.6 degrees of freedom. True or false: this must be a software error, because degrees of freedom are always whole numbers.

True or false.

• True
• False

Of 333 sexed penguins, 165 are female. You test H₀: p = 0.5 against Hₐ: p ≠ 0.5 with a one-proportion z test. Which standard error does the test use?

Select one.

• √(p₀(1 − p₀) ⁄ n), with the null value p₀ = 0.5
• √(p̂(1 − p̂) ⁄ n), with the sample share p̂
• s ⁄ √n, with s the sample standard deviation
• √(p̂_pool(1 − p̂_pool)(1 ⁄ n₁ + 1 ⁄ n₂))

For the 333 sexed penguins (165 female), the one-proportion z test of H₀: p = 0.5 gives z = −0.164 and a two-sided p-value of about 0.87. Which conclusion is correct at α = 0.05?

Select one.

• The data prove that exactly half of the penguins are female.
• There is about an 87% chance that H₀ is true for these penguins.
• Fail to reject H₀; the data are consistent with an even split.
• The penguins show no difference at all from an even split.

On Biscoe, 44 of 168 penguins are Adelie (about 26.2%); on Dream, 56 of 124 are Adelie (about 45.2%). What is the pooled proportion used in the two-proportion z test?

Select one.

• About 19.0%
• About 34.2%
• About 35.7%
• About 26.2%

The two-proportion z test comparing the Adelie share on Biscoe and Dream gives z ≈ −3.38. The critical values are z* = 1.960 for α = 0.05 and z* = 2.576 for α = 0.01. Which decision is correct?

Select one.

• Fail to reject H₀ at both levels
• Reject H₀ at α = 0.05 only
• Fail to reject at 0.05, reject at 0.01
• Reject H₀ at both α = 0.05 and α = 0.01

The 95% t interval for the mean body mass μ of Adelie penguins runs from 3,626.92 g to 3,774.40 g. Which claimed value of μ would a two-sided test at α = 0.05 reject?

Select one.

• 4,000 g
• 3,750 g
• 3,700.66 g
• 3,733.09 g

Suppose a poll of 1,000 adults finds 54% support for a proposal. The test of H₀: p = 0.5 gives z ≈ 2.53. The 95% interval runs from 50.9% to 57.1%, and the 99% interval runs from 49.93% to 58.07%. Select every statement that is true.

Select every option that applies.

• The test rejects H₀ at α = 0.05.
• The 95% interval excludes 50%.
• The test rejects H₀ at α = 0.01.
• The 99% interval excludes 50%.
• The p-value is the probability that H₀ is true.