Sampling Distributions: 21-30

Which of the following statements is incorrect?

• The larger the sample, the larger the spread in the sampling distribution.

• Provided that the population size is significantly greater than the sample size, the spread of a sampling distribution is about the same no matter what the population size.

• Bias has to do with the center, not the spread, of a sampling distribution.

• Sample distribution and sampling distribution refer to different things.

• The larger the sample, the closer the sample distribution generally becomes to the population distribution.

Which of the following statements is incorrect?

Suppose the average outstanding loan for college graduates is $23,500 with a standard deviation of $7,200. In an SRS of 50 graduating college students, what is the probability that their mean outstanding loan is under $21,000?

Tags

CCSS.HSS.ID.A.4

Which of the following is a true statement?

• The sampling distribution of p̂ has a mean that can vary from the population proportion p by approximately 1.96 standard deviations.

• The sample proportion is a random variable with a probability distribution.

• None of the others are a true statement.

• has a normal distribution.

• has a t-distribution with df=5.

• has a t-distribution with df=4.

• has neither a normal distribution nor a t-distribution.

• has either a normal distribution or a t-distribution depending on the characteristics of the population standard deviation.

Suppose 56 percent of eight-to-twelve-year-olds expect to have "a great life". In an SrS of 125 eight-to-twelve-year-olds, what is the probability that between 50 percent and 60 percent will say they expect to have "a great life"?

Tags

CCSS.HSS.IC.B.4

Which of the following are unbiased estimators for the corresponding population parameters?

I. Sample means

II. Sample proportions

III. Difference of sample means

IV. Difference of sample proportions

• None are unbiased.

• I and II

• I and III

• III and IV

• All are unbiased.

Answer explanation

All are unbiased estimators for the corresponding population parameters; that is, the means of their sampling distributions are equal to the population parameters.

Which of the following statements is incorrect?

• Sample statistics are used to make inferences about population parameters.

• Statistics from smaller samples have more variability.

• Parameters are fixed, while statistics vary depending on which sample is chosen.

• As the sample size n becomes larger, the sample distribution becomes closer to a normal distribution.

• All other statements are true.

Tags

CCSS.6.SP.A.2

A new soft drink product has an average number of 77 calories per bottle with a standard deviation of 4.5 calories. In a random sample of 40 bottles, what is the probability that the mean number of calories is between 75 and 80?

Tags

CCSS.HSS.ID.A.4

Which of the following statements is true?

• The mean of the set of sample means varies inversely with the square root of the samples.

• The variance of the set of sample means varies directly with the size of the samples and inversely with the variance of the population.

• The standard deviation of the set of sample means varies directly with the standard deviation of the original population and inversely with the square root of the size of the samples.

• The larger the sample size, the larger the variance of the set of sample means.