Week 12 Quiz

Of the 333 penguins in the Palmer field study with a recorded sex, 165 are female and 168 are male, so p̂ = 0.4955. Which fact satisfies the large-counts condition for a one-proportion z interval for p, the share of females among all penguins like these?

Select one.

• The sample has 333 penguins, well above 30.
• The sample proportion 0.4955 is close to the even split of 0.5.
• There are 165 females and 168 males, both at least 10.
• The penguins were studied in a field study.

Of the 333 penguins in the Palmer field study with a recorded sex, 165 are female and 168 are male, so p̂ = 0.4955. The standard error of p̂ is SE = 0.0274, and the critical value for 95% is z* = 1.960. What is the margin of error? Enter it as a proportion rounded to four decimals, such as 0.1234.

Type a short answer.

Of the 333 penguins in the Palmer field study with a recorded sex, 165 are female and 168 are male, so p̂ = 0.4955. With SE = 0.0274 and z* = 1.960 for 95%, which is the 95% one-proportion z interval for p?

Select one.

• 0.4681 to 0.5229
• 0.4418 to 0.5492
• 0.4940 to 0.4970
• 0.4504 to 0.5406

The 95% one-proportion z interval for the share of female penguins runs from 0.4418 to 0.5492. Which sentence interprets it correctly?

Select one.

• There is a 95% probability that the population proportion lies between 0.4418 and 0.5492.
• About 95% of penguins are between 0.4418 and 0.5492 female.
• About 95% of sample proportions will fall between 0.4418 and 0.5492.
• We are 95% confident that the population proportion of female penguins is between 0.4418 and 0.5492.

True or false: because 0.5 lies inside the 95% interval 0.4418 to 0.5492, the data prove that exactly half of the penguins in the population are female.

True or false.

• True
• False

For a poll with a share near 0.5, the 95% margin of error is 0.098 with 100 people. Using the course's poll ladder, what is the 95% margin of error with 400 people?

Select one.

• 0.049
• 0.0245
• 0.0693
• 0.0196

A pollster has no earlier estimate of the share and wants a 95% margin of error of plus or minus 3 percentage points. Using the conservative p̂ = 0.5 and z* = 1.96, how many people should the poll include? Enter a whole number only.

Type a short answer.

A news poll reports that 52% of residents support a new bus line, with a margin of error of plus or minus 3 percentage points. Which range does that margin describe?

Select one.

• 49% to 55%
• 50.44% to 53.56%
• 51.97% to 52.03%
• 3% to 55%

A news site's online poll drew 10,000 readers who chose to click an answer, so its conservative 95% margin of error is a little under 1 percentage point. Which statement is correct?

Select one.

• The margin of error already accounts for the many readers who saw the poll but chose not to click.
• The poll is accurate to within about 1 percentage point of the true share.
• The margin covers sampling variability only, so voluntary-response bias can make the poll miss by much more.
• A sample of 20,000 clicks would remove the bias.

A phone survey of a random sample of 1,000 adults reports a 95% margin of error of about 3.1 percentage points. Select every source of error that this margin of error does NOT cover.

Select every option that applies.

• Non-response bias, when many chosen adults never answer and differ from those who do
• Question-wording bias, when the wording pushes people toward one answer
• Undercoverage, when some adults have no phone and cannot be reached
• The chance variation from which random sample of 1,000 happened to be drawn
• The sample-to-sample wobble of p̂ that shrinks as the sample size grows