Consider the probability distribution shown here. $\begin{array}{l|rrr} \hline x & 0 & 2 & 4 \\ \hline p(x) & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \hline \end{array}$ Let $\bar { x }$ be the sample mean for random samples of $n = 2$ measurements from this distribution. Find $E ( x )$ and $E ( \bar { x } )$.

\[\begin{array} { l } E ( x ) = \mu = (

The probability distribution shown below describes a population of measurements that can assume values of 5, 9, 13, and 17, each of which occurs with the same frequency: $\begin{array}{c|cccc} \hline x & 5 & 9 & 13 & 17 \\ \hline p(x) & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} \\ \hline \end{array}$ Find $E ( x ) = \mu$. Then consider taking samples of $n = 2$ measurements and calculating $\bar { x }$ for each sample. Find the expected value, $E ( \bar { x } )$, of $\bar { x }$.

\[\begin{array} { l } E ( x ) = ( 5 ) \

Exam 5: Sampling Distributions

A point estimator of a population parameter is a rule or formula which tells us how to use sample data to calculate a single number that can be used as an estimate of the population parameter.

(True/False)

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Question 21

Suppose students' ages follow a skewed right distribution with a mean of 23 years old and a standard deviation of 4 years. If we randomly sample 200 students, which of the following Statements about the sampling distribution of the sample mean age is incorrect?

(Multiple Choice)

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Question 22

Which of the following statements about the sampling distribution of the sample mean is incorrect?

(Multiple Choice)

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Question 23

Suppose a random sample of $n = 36$ measurements is selected from a population with mean $\mu = 256$ and variance $\sigma ^ { 2 } = 144$ . Find the mean and standard deviation of the sampling distribution of the sample mean $\bar { x }$ .

(Essay)

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Question 24

The sample mean, $\bar{x}$ , is a statistic.

(True/False)

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Question 25

If $\bar{x}$ is a good estimator for µ, then we expect the values of x to cluster around µ.

(True/False)

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Question 26

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

(True/False)

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Question 27

Consider the population described by the probability distribution below. x 3 5 7 p(x) .1 .7 .2 a. Find $\mu$ . b. Find the sampling distribution of the sample median for a random sample of $n = 2$ observations from this population. c. Show that the median is an unbiased estimator of $\mu$ .

(Essay)

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Question 28

The probability of success, p, in a binomial experiment is a parameter, while the mean and standard deviation, µ and ?, are statistics.

(True/False)

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Question 29

The length of time a traffic signal stays green (nicknamed the "green time") at a particular intersection follows a normal probability distribution with a mean of 200 seconds and the standard Deviation of 10 seconds. Use this information to answer the following questions. Which of the Following describes the derivation of the sampling distribution of the sample mean?

(Multiple Choice)

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Question 30

Consider the probability distribution shown here. x 0 2 4 p(x) Let $\bar { x }$ be the sample mean for random samples of $n = 2$ measurements from this distribution. Find $E ( x )$ and $E ( \bar { x } )$ .

(Essay)

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Question 31

The standard error of the sampling distribution of the sample mean is equal to ?, the standard deviation of the population.

(True/False)

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Question 32

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

(Multiple Choice)

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Question 33

A random sample of $n = 600$ measurements is drawn from a binomial population with probability of success $.08$ . Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$ .

(Multiple Choice)

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Question 34

The probability distribution shown below describes a population of measurements that can assume values of 5, 9, 13, and 17, each of which occurs with the same frequency: x 5 9 13 17 p(x) Find $E ( x ) = \mu$ . Then consider taking samples of $n = 2$ measurements and calculating $\bar { x }$ for each sample. Find the expected value, $E ( \bar { x } )$ , of $\bar { x }$ .

(Essay)

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Question 35

Consider the population described by the probability distribution below. x 3 5 7 p(x) .1 .7 .2 a. Find $\sigma ^ { 2 }$ . b. Find the sampling distribution of the sample variance $s ^ { 2 }$ for a random sample of $n = 2$ measurements from the distribution. c. Show that $s ^ { 2 }$ is an unbiased estimator of $\sigma ^ { 2 }$ .

(Essay)

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Question 36

A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success .26. Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$ .

(Multiple Choice)

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Question 37

The ideal estimator has the greatest variance among all unbiased estimators.

(True/False)

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Question 38

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

(True/False)

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Question 39

The weight of corn chips dispensed into a 14-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 14.5 ounces and a standard deviation of 0.2 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 14.6 ounces.

(Multiple Choice)

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Question 40

Showing 21 - 40 of 52

A point estimator of a population parameter is a rule or formula which tells us how to use sample data to calculate a single number that can be used as an estimate of the population parameter.

Suppose students' ages follow a skewed right distribution with a mean of 23 years old and a standard deviation of 4 years. If we randomly sample 200 students, which of the following Statements about the sampling distribution of the sample mean age is incorrect?

Which of the following statements about the sampling distribution of the sample mean is incorrect?

Suppose a random sample of $n = 36$ measurements is selected from a population with mean $\mu = 256$ and variance $\sigma ^ { 2 } = 144$ . Find the mean and standard deviation of the sampling distribution of the sample mean $\bar { x }$ .

The sample mean, $\bar{x}$ , is a statistic.

If $\bar{x}$ is a good estimator for µ, then we expect the values of x to cluster around µ.

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

Consider the population described by the probability distribution below. x 3 5 7 p(x) .1 .7 .2 a. Find $\mu$ . b. Find the sampling distribution of the sample median for a random sample of $n = 2$ observations from this population. c. Show that the median is an unbiased estimator of $\mu$ .

The probability of success, p, in a binomial experiment is a parameter, while the mean and standard deviation, µ and ?, are statistics.

Consider the probability distribution shown here. x 0 2 4 p(x) Let $\bar { x }$ be the sample mean for random samples of $n = 2$ measurements from this distribution. Find $E ( x )$ and $E ( \bar { x } )$ .

The standard error of the sampling distribution of the sample mean is equal to ?, the standard deviation of the population.

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

A random sample of $n = 600$ measurements is drawn from a binomial population with probability of success $.08$ . Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$ .

A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success .26. Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$ .

The ideal estimator has the greatest variance among all unbiased estimators.

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

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Exam 5: Sampling Distributions

A point estimator of a population parameter is a rule or formula which tells us how to use sample data to calculate a single number that can be used as an estimate of the population parameter.

Suppose students' ages follow a skewed right distribution with a mean of 23 years old and a standard deviation of 4 years. If we randomly sample 200 students, which of the following Statements about the sampling distribution of the sample mean age is incorrect?

Which of the following statements about the sampling distribution of the sample mean is incorrect?

Suppose a random sample of n=36n = 36n=36 measurements is selected from a population with mean μ=256\mu = 256μ=256 and variance σ2=144\sigma ^ { 2 } = 144σ2=144 . Find the mean and standard deviation of the sampling distribution of the sample mean xˉ\bar { x }xˉ .

The sample mean, xˉ\bar{x}xˉ , is a statistic.

If xˉ\bar{x}xˉ is a good estimator for µ, then we expect the values of x to cluster around µ.

As the sample size gets larger, the standard error of the sampling distribution of the sample mean gets larger as well.

Consider the population described by the probability distribution below. x 3 5 7 p(x) .1 .7 .2 a. Find μ\muμ . b. Find the sampling distribution of the sample median for a random sample of n=2n = 2n=2 observations from this population. c. Show that the median is an unbiased estimator of μ\muμ .

The probability of success, p, in a binomial experiment is a parameter, while the mean and standard deviation, µ and ?, are statistics.

Consider the probability distribution shown here. x 0 2 4 p(x) Let xˉ\bar { x }xˉ be the sample mean for random samples of n=2n = 2n=2 measurements from this distribution. Find E(x)E ( x )E(x) and E(xˉ)E ( \bar { x } )E(xˉ) .

The standard error of the sampling distribution of the sample mean is equal to ?, the standard deviation of the population.

The Central Limit Theorem states that the sampling distribution of the sample mean is approximately normal under certain conditions. Which of the following is a necessary condition for the Central Limit Theorem to be used?

A random sample of n=600n = 600n=600 measurements is drawn from a binomial population with probability of success .08.08.08 . Give the mean and the standard deviation of the sampling distribution of the sample proportion, p^\hat { p }p^​ .

A random sample of n=300\mathrm { n } = 300n=300 measurements is drawn from a binomial population with probability of success .26. Give the mean and the standard deviation of the sampling distribution of the sample proportion, p^\hat { p }p^​ .

The ideal estimator has the greatest variance among all unbiased estimators.

The Central Limit Theorem guarantees that the population is normal whenever n is sufficiently large.

Statistics, Data, and Statistical Thinking

Methods for Describing Sets of Data

Probability

Random Variables and Probability Distributions

Inferences Based on a Single Sample: Estimation With Confidence Intervals

Inferences Based on a Single Sample: 355 Tests of Hypotheses

Inferences Based on Two Samples: Confidence Intervals and Tests of Hypotheses

Design of Experiments and Analysis of Variance

Categorical Data Analysis

Simple Linear Regression

Multiple Regression and Model Building

Methods for Quality Improvement: Statistical Process Control Available on CD

Time Series: Descriptive Analyses, Models, and Forecasting Available on CD

Nonparametric Statistics Available on CD

Filters

Suppose a random sample of $n = 36$ measurements is selected from a population with mean $\mu = 256$ and variance $\sigma ^ { 2 } = 144$ . Find the mean and standard deviation of the sampling distribution of the sample mean $\bar { x }$ .

The sample mean, $\bar{x}$ , is a statistic.

If $\bar{x}$ is a good estimator for µ, then we expect the values of x to cluster around µ.

Consider the population described by the probability distribution below. x 3 5 7 p(x) .1 .7 .2 a. Find $\mu$ . b. Find the sampling distribution of the sample median for a random sample of $n = 2$ observations from this population. c. Show that the median is an unbiased estimator of $\mu$ .

Consider the probability distribution shown here. x 0 2 4 p(x) Let $\bar { x }$ be the sample mean for random samples of $n = 2$ measurements from this distribution. Find $E ( x )$ and $E ( \bar { x } )$ .

A random sample of $n = 600$ measurements is drawn from a binomial population with probability of success $.08$ . Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$ .

A random sample of $\mathrm { n } = 300$ measurements is drawn from a binomial population with probability of success .26. Give the mean and the standard deviation of the sampling distribution of the sample proportion, $\hat { p }$ .