Exam 9: Sampling Distributions

In an effort to identify the true proportion of college freshman who are under 18 years of age, a random sample of 500 freshmen was taken. Fifty of them were under the age of 18. The value 0.10 is a point estimate of the true proportion of freshman under age 18.

(True/False)

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Question 81

The accuracy of the approximation of $\bar { X }$ with a normal distribution depends on the probability distribution of the and on the sample .

(Short Answer)

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Question 82

NARRBEGIN: Mean Salary Mean Salary In order to estimate the mean salary for a population of 500 employees, the president of a certain company selected at random a sample of 40 employees.NARREND -{Mean Salary Narrative} If the population standard deviation is $800, compute the standard error both with and without using the finite population correction factor.

(Essay)

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Question 83

For sample sizes greater than 30, the sampling distribution of the mean is approximately normally distributed:

(Multiple Choice)

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Question 84

NARRBEGIN: Heights of Men Heights of Men The heights of men in the USA are normally distributed with a mean of 68 inches and a standard deviation of 4 inches.NARREND -{Heights of Men Narrative} A random sample of five men is selected. What is the probability that the sample mean is greater than 70 inches?

(Short Answer)

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Question 85

NARRBEGIN: Graduate Internships Graduate Internships The chairman of the Biology department in a certain college believes that 70% of the department's graduate internships are given to international students. A random sample of 50 graduate interns is taken.NARREND -{Graduate Internships Narrative} Assume that the chairman is correct and p = 0.70. What is the sampling distribution of the sample proportion $\tilde{ p }$ ? Explain.

(Essay)

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Question 86

NARRBEGIN: PokerTime Poker Time The amount of time spent by American adults playing Poker per week is normally distributed with a mean of 4 hours and standard deviation of 1.25 hours.NARREND -{Poker Time Narrative} Find the probability that if four American adults are randomly selected, their average number of hours spent playing Poker is more than 5 hours per week.

(Short Answer)

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Question 87

Because the value of the ____________________ varies from sample to sample, we can regard it as a new random variable, created by sampling.

(Short Answer)

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Question 88

NARRBEGIN: Temporary Worker Producti Temporary Worker Productivity A temporary worker productivity is normally distributed. One worker produces an average of 84 units per day with a standard deviation of 24. Another worker produces at an average rate of 74 per day with a standard deviation of 25.NARREND -{Temporary Worker Productivity Narrative} What is the probability that during one week (5 working days), worker 1 will outproduce worker 2 on average?

(Essay)

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Question 89

Given that X is a binomial random variable with very large n, the binomial probability P(X = 5) is approximated by the area under a normal curve between

(Multiple Choice)

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Question 90

In general, the binomial probability P(X = x) is approximated by the area under a normal curve between x - .5 and x + .5.

(True/False)

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Question 91

NARRBEGIN: CFO's Salary CFO's Salary Suppose that the starting salaries of female CFO's have a positively skewed distribution with mean of $56,000 and a standard deviation of $12,000. The starting salaries of male CFO's are positively skewed with a mean of $50,000 and a standard deviation of $10,000. A random sample of 50 female CFO's and a random sample of 40 male CFO's are selected.NARREND -{CFO's Salary Narrative} Find the expected value of the sample mean difference.

(Essay)

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Question 92

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

(Multiple Choice)

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Question 93

NARRBEGIN: CFO's Salary CFO's Salary Suppose that the starting salaries of female CFO's have a positively skewed distribution with mean of $56,000 and a standard deviation of $12,000. The starting salaries of male CFO's are positively skewed with a mean of $50,000 and a standard deviation of $10,000. A random sample of 50 female CFO's and a random sample of 40 male CFO's are selected.NARREND -Two samples are selected independently from two normal populations and the mean and standard error of the sampling distribution of $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ are 32 and 38.72, respectively. Calculate P( $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ > 0).

(Essay)

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Question 94

The mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to the mean of the difference $\bar { X } _ { 2 } - \bar { X } _ { 1 }$ .

(True/False)

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Question 95

Sampling distributions describe the distributions of:

(Multiple Choice)

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Question 96

NARRBEGIN: DVD Rental Store DVD Rental Store A DVD rental store wants to know what proportion of its customers are under age 21. A simple random sample of 500 customers was taken, and 375 of them were under age 21. Presume that the true population proportion of customers under age 21 is 0.68.NARREND -Given a binomial random variable with n = 15 and p = .40, find the exact probabilities of the following events and their normal approximations. a.X = 6 b.X $\ge$ 9 c.X $\le$ 10

(Essay)

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Question 97

An infinite population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:

(Multiple Choice)

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Question 98

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to:

(Multiple Choice)

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Question 99

The expected value of $\tilde{ p }$ is ____________________.

(Short Answer)

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Question 100

Showing 81 - 100 of 154

In an effort to identify the true proportion of college freshman who are under 18 years of age, a random sample of 500 freshmen was taken. Fifty of them were under the age of 18. The value 0.10 is a point estimate of the true proportion of freshman under age 18.

The accuracy of the approximation of $\bar { X }$ with a normal distribution depends on the probability distribution of the and on the sample .

For sample sizes greater than 30, the sampling distribution of the mean is approximately normally distributed:

Because the value of the ____________________ varies from sample to sample, we can regard it as a new random variable, created by sampling.

Given that X is a binomial random variable with very large n, the binomial probability P(X = 5) is approximated by the area under a normal curve between

In general, the binomial probability P(X = x) is approximated by the area under a normal curve between x - .5 and x + .5.

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

The mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to the mean of the difference $\bar { X } _ { 2 } - \bar { X } _ { 1 }$ .

Sampling distributions describe the distributions of:

An infinite population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to:

The expected value of $\tilde{ p }$ is ____________________.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Multiple Regression

Filters

Exam 9: Sampling Distributions

In an effort to identify the true proportion of college freshman who are under 18 years of age, a random sample of 500 freshmen was taken. Fifty of them were under the age of 18. The value 0.10 is a point estimate of the true proportion of freshman under age 18.

The accuracy of the approximation of Xˉ\bar { X }Xˉ with a normal distribution depends on the probability distribution of the ____________________ and on the sample ____________________.

For sample sizes greater than 30, the sampling distribution of the mean is approximately normally distributed:

Because the value of the ____________________ varies from sample to sample, we can regard it as a new random variable, created by sampling.

Given that X is a binomial random variable with very large n, the binomial probability P(X = 5) is approximated by the area under a normal curve between

In general, the binomial probability P(X = x) is approximated by the area under a normal curve between x - .5 and x + .5.

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if

The mean of the difference Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​ is equal to the mean of the difference Xˉ2−Xˉ1\bar { X } _ { 2 } - \bar { X } _ { 1 }Xˉ2​−Xˉ1​ .

Sampling distributions describe the distributions of:

An infinite population has a mean of 40 and a standard deviation of 15. A sample of size 100 is taken at random from this population. The standard error of the sample mean equals:

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the difference Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​ is equal to:

The expected value of p~\tilde{ p }p~​ is ____________________.

What Is Statistics

Graphical Descriptive Techniques I

Graphical Descriptive Techniques II

Numerical Descriptive Techniques

Data Collection and Sampling

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Introduction to Estimation

Introduction to Hypothesis Testing

Inference About a Population

Inference About Comparing Two Populations

Analysis of Variance

Chi-Squared Tests Optional

Simple Linear Regression and Correlation

Multiple Regression

Filters

The accuracy of the approximation of $\bar { X }$ with a normal distribution depends on the probability distribution of the and on the sample .

The mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to the mean of the difference $\bar { X } _ { 2 } - \bar { X } _ { 1 }$ .

If two random samples of sizes 30 and 36 are selected independently from two populations with means 78 and 85, and standard deviations 12 and 15, respectively, then the mean of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to:

The expected value of $\tilde{ p }$ is ____________________.