Chapter 6 Sampling Distribution Practice Test

A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the following statements is true about these percentages?

• 72% and 56% are both statistics.

• 72% is a statistic and 56% is a parameter.

• 72%is a parameter and 56% is a statistic.

• 72% and 56% are both parameters.

Tags

CCSS.HSS.IC.B.3

Suppose a Vermont state trooper randomly selects 50 cars driving past an exit, records the state on the license plate and calculates the proportion of cars with out-of-state plates. Which of the following describes the sampling distribution of the sample proportion in this context?

• The distribution of state for all cars in the trooper's sample of cars passing this exit.

• The distribution of state for all cars passing this exit.

• The distribution of the proportion of cars with out-of-state plates in all possible samples of 50 cars passing this exit.

• The distribution of the proportion of cars with out-of-state plates in the trooper's sample of 50 cars passing this exit.

A polling organization wants to estimate the proportion of voters who favor a new law banning smoking in public buildings. The organization decides to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The effect of this increase is to

• reduce the bias of the estimate.

• increase the bias of the estimate.

• reduce the variability of the estimate.

• increase the variability of the estimate.

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

A machine is designed to fill 16 oz bottles of shampoo. When the machine is working properly, the amount poured into the bottles follows a normal distribution with mean 16.05 oz and standard deviation 0.1 oz. Assume that the machine is working properly. If 4 bottles are randomly selected and the number of ounces in each bottle is measured, then there is about a 95% chance that the sample mean will fall in which of the following intervals?

• 16.00 to 16.10 ounces

• 15.95 to 16.15 ounces

• 15.90 to 16.20 ounces

• 15.85 to 16.25 ounces

The central limit theorem is important in statistics because it allows us to use the normal distribution to find probabilities involving the sample mean if the

• sample size is reasonably large for any population shape.

• sample size is reasonably large and the population is normally distributed.

• population size is reasonably large for any population shape.

• population size is reasonably large and the population is normally distributed.

Tags

CCSS.HSS.ID.A.4

At a high school, 85% of students are right-handed. Let X = the number of students who are right-handed in a random sample of 10 students from the school. Which one of the following statements about the mean and standard deviation of the sampling distribution of X is true?

• μ_x = 8.5; σ_x ≈ 1.129

• μ_x = 8.5; σ_x ≈ 0.113

• μ_x = 8.5; σ_x cannot be determined from the information given.

• Neither the mean nor the standard deviation can be determined from the information given.

The student newspaper at a large university asks an SRS of 250 undergraduates, "Do you favor eliminating the carnival from the end-of-term celebration?" In the sample, 150 of the 250 undergraduates are in favor. Suppose that 55% of all undergraduates favor eliminating the carnival. If you took a very large number of SRSs of size n = 250 from this population, the sampling distribution of the sample proportion, p-hat would have which of the following characteristics?

• Mean 0.55, standard deviation 0.03, shape unknown

• Mean 0.55, standard deviation 0.03, approximately normal

• Mean 0.60, standard deviation 0.03, shape unknown

• Mean 0.60, standard deviation 0.03, approximately normal

Scores on the mathematics part of the SAT exam in a recent year followed a normal distribution with mean 515 and standard deviation 114. You choose an SRS of 100 students and calculate x̅, the mean SAT math score. Which of the following are the mean and standard deviation of the sampling distribution of x̅?

• mean = 515, sd = 114

• mean = 515, sd = 114/√100

• mean = 515/100, sd = 114/100

• mean = 515/100, sd = 114/√100

In a congressional district, 55% of the registered voters are Democrats. Which of the following is closest to the probability of getting less than 50% Democrats in a random sample of size 100?

• 0.157

• 0.496

• 0.504

• 0.843

Tags

CCSS.HSS.ID.A.4

A statistic is an unbiased estimator of a parameter when

• the statistic is calculated from a random sample.

• in all possible samples of a specific size, the distribution of the statistic has a shape that is approximately normal.

• in all possibles samples of a specific size, the values of the statistic are very close to the value of the parameter.

• in all possible samples of a specific size, the values of the statistic are centered at the value of the parameter.