Week 11 Quiz

A field team weighed 151 Adelie penguins: the sample mean is x̄ = 3,700.66 g and the sample standard deviation is s = 458.57 g. Which value is the point estimate of μ, the mean body mass of all Adelie penguins like these?

Select one.

• x̄ = 3,700.66 g
• s = 458.57 g
• The range 3,626.92 g to 3,774.40 g
• μ itself, which the sample reveals exactly

A field team weighed 151 Adelie penguins: the sample mean is x̄ = 3,700.66 g and the sample standard deviation is s = 458.57 g. How many degrees of freedom does the one-sample t interval for μ use?

Select one.

• 151
• 152
• 150
• 149

A field team weighed 151 Adelie penguins: the sample mean is x̄ = 3,700.66 g and the sample standard deviation is s = 458.57 g. Its standard error is SE = 37.32 g, and the critical value for 95% with df = 150 is t* = 1.976. What is the margin of error, in grams? Enter the number rounded to two decimals, with no units.

Type a short answer.

A field team weighed 151 Adelie penguins: the sample mean is x̄ = 3,700.66 g and the sample standard deviation is s = 458.57 g. With SE = 37.32 g and t* = 1.976 for 95% with df = 150, which is the 95% t interval for μ?

Select one.

• 3,242.09 g to 4,159.23 g
• 3,694.66 g to 3,706.66 g
• 3,697.62 g to 3,703.70 g
• 3,626.92 g to 3,774.40 g

The 95% t interval for the mean body mass of Adelie penguins runs from 3,626.92 g to 3,774.40 g. Which sentence interprets it correctly?

Select one.

• There is a 95% probability that the population mean lies between 3,626.92 g and 3,774.40 g.
• We are 95% confident that the population mean body mass of Adelie penguins is between 3,626.92 g and 3,774.40 g.
• About 95% of Adelie penguins weigh between 3,626.92 g and 3,774.40 g.
• About 95% of sample means will fall between 3,626.92 g and 3,774.40 g.

True or false: once the interval 3,626.92 g to 3,774.40 g has been computed, there is a 95% probability that the population mean μ lies inside it.

True or false.

• True
• False

Using the course's critical values for 95% confidence (2.262 at df 9, 2.064 at df 24, 1.976 at df 150, and z* = 1.960), which t* belongs to a sample of 25 birds?

Select one.

• 2.262
• 2.064
• 1.976
• 1.960

A field team weighed 151 Adelie penguins: the sample mean is x̄ = 3,700.66 g and the sample standard deviation is s = 458.57 g. Which number measures how much the sample mean typically wobbles from one sample of 151 birds to the next?

Select one.

• 458.57 g
• 73.74 g
• 37.32 g
• 147.48 g

A field team plans a new 95% t interval for the mean mass of Adelie penguins. Holding everything else the same, which change would make the margin of error smaller?

Select one.

• Weighing more birds
• Raising the confidence level to 99%
• Studying a group whose masses vary more
• Weighing 10 birds instead of 151

A field team weighed 151 Adelie penguins: the sample mean is x̄ = 3,700.66 g and the sample standard deviation is s = 458.57 g. The birds were weighed in a field study, not drawn at random. Select every statement that correctly supports or limits the use of a one-sample t interval here.

Select every option that applies.

• A sample of 151 is far above the rule of thumb of about 30, so the sampling distribution of x̄ is approximately normal.
• Each bird is weighed separately, so one mass does not set another.
• Because the sample is large, any bias in how the birds were found is removed.
• Because the sample is large, the individual body masses must follow a normal model.