Chapter 7 Quiz

According to a recent poll, 92% of Americans believe more could be done to end the pandemic. Let's assume this is the parameter value for the population. If you take an SRS of 65 Americans and let p̂ = the proportion in the sample who feel more could be done, is the shape of the sampling distribution of p̂ approximately Normal?

• Yes, because n ≥ 30

• Yes, because np = 59.8

• No, because n(1-p) = 5.2

• No, because 65 ≤ 1/10 N

The time it takes all cross country runners to complete a course has a mean of 32.1 minutes with a standard deviation of 10.2 minutes. What is the probability that an SRS of 36 runners will have a mean completion time greater than 34 minutes?

• .4261

• .5739

• .8681

• .1319

A Gallup Poll asked a random sample of 1240 adults, "Do you play video games?" Suppose the true proportion of all adults who play video games

is p = .26.
What is the standard deviation of the sampling distribution of p̂?  Check that the 10% condition is met.

• The 10% condition is met.  σp̂ = .0126

• The 10% condition is not met.

• The 10% condition is met.  σp̂ = .0074

• The 10% condition is met.  σp̂ = .26

To find the proportion of students who have taken a COVID test, an SRS of 400 students was taken from an area high school with a population of 1600 students. The statewide proportion of students who have taken a COVID test is p = .48. What is the standard deviation of the sampling distribution?

• .0250

• The Large Counts Condition is not met.

• The 10% Condition is not met.

• .0412

The distribution of GPA's for all AP Statistics students is skewed to the left with a population mean, μ = 3.68 and a standard deviation, σ = 1.2. An SRS of 30 AP Statistics students was taken. The shape and standard deviation of the sampling distribution is

• Normal with a σ_x = .2191

• Normal with a σ_x = 1.2

• Skewed to the left with a σ_x = .2191

• The 10% Condition is not met

In a recent state election, 58% of the voters were Democratic. The total percent of Democratic voters in the state is actually 52%.

• 52% is a statistic and 58% is a parameter.

• 52% is a parameter and 58% is a statistic.

• I am unable to determine parameters with the given information.

• Both 52% and 58% are parameters.

When the mean of a sampling distribution is the same as that of the population, we say that

• it is an unbiased estimator of the population

• it is an unbiased estimator of the statistic

• it is a low variability estimator of the population

• it is a biased estimator of the population

When x̅ differs from sample to sample, we say this is an example of

• variability among the samples

• bias among the samples

• not having large enough sample sizes

• poor survey techniques

The Central Limit Theorem allows us to use Normal distributions to find probabilities involving the sample mean

• when n ≥ 30

• when n ≤ 30

• when np ≤ 10 and n(1-p) ≤ 10

• when the population is 10 times greater than the sample size

A certain Boba machine is designed to fill a 16-ounce cup. When it is working properly, the amount filled follows a Normal distribution with a mean of 16.5 ounces and a standard deviation of 0.3 ounces. If 4 cups of Boba are randomly selected, what is the probability that the sample mean will be less than 16.8 ounces?

• .9772

• .1587

• .8413

• .0228