Sampling Distribution Practice MC

For a particular population, the sampling distribution of the sample mean for random samples of size 25 has a mean of 125 and a standard deviation of 30. What are the mean and standard deviation of the population?

• mean=5

  Standard deviation=6

• mean = 5, standard deviation = 30

• mean = 125, standard deviation = 6

• mean = 125, standard deviation =30

• mean = 125, standard deviation = 150

According to a recent poll, 27% of Americans get 30 minutes of exercise at least five days each week.  Let’s assume this is the parameter value for the population.  If you take a simple random sample of 25 Americans and let p-hat = the proportion in the sample who get 30 minutes of exercise at least five days per week, is the shape of the sampling distribution of approximately Normal?

• No, because n<30

• No, because np<10

• Yes, because we can reasonably assume that there are more than (10)(25)=250 individuals in the population

• Yes, because we took a simple random sample

If we took an SRS of 1700 people from California (population 34 million) and an SRS of 1000 people from Detroit (population 1 million) which sampling distribution would have the smaller standard deviation?

• Detroit, because 1000 out of 1,000,000 is more than 1700 out of 32,000,000

• Detroit, because it has a smaller population size

• California, because the sample size(1700) is larger than the sample size for Detroit

• California, because it has a larger population size

• They would be the same because simple random samples are takin in both places

To the left are dot plots of the values taken by three different statistics estimating the same parameter in 30 samples from the same population. The true value of the population parameter is marked with an arrow. Based on the performance of the three statistics in many samples, which is preferred as an estimate of the parameter?

• Statistic A

• Statistic B

• Statistic C

• Either Statistic A or Statistic B would be equally good.

• Either Statistic B or Statistic C would be equally good.

Tags

CCSS.6.SP.A.3

According to the DuPont 2016 Global Automotive Color Popularity Report, 23% of all cars manufactured in 2016 were white.  In a random sample of 100 cars parked in long-term parking at Philadelphia International Airport, 19% of the cars were white.  Which statement is true?

• 19% and 23% are parameters, 100 is a statistic

• 23% is a parameter, 19% is a statistic

• 23% is a statistic, 19% is a parameter

• 19% and 23% are statistics, 100 is neither a parameter nor a statistic

• 19%, 23%, and 100 are all statistics

Tags

CCSS.HSS.IC.B.3

Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let X be the number of successes in the sample. For which value of p would it be safe to assume the sampling distribution of X is approximately normal?

• 0.01

• 0.099

• 0.111

• 0.975

• 0.9999

Tags

CCSS.HSS.IC.B.4

A survey asks a simple random sample of 500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education.  Let p-hat denote the proportion in the sample who say they support the increase.  Suppose that 53% of all adults in Ohio support the increase.  What is the probability that less than half the sample will say they support the increase?

Tags

CCSS.HSS.ID.A.4