The following table gives the number of pets owned for a population of four families. $\begin{array} { | l | c | c | c | c | } \hline \text { Family } & \text { A } & \text { B } & \text { C } & \text { D } \\ \hline \text { Number of pets owned } & 2 & 1 & 4 & 3 \\ \hline \end{array}$ Find the mean and standard deviation for the population.

The answer of The following table gives the number of...

A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true? $\begin{array}{|l|l|} \hline A&\text {The population standard deviation decreases. }\\ \hline B&\text {The standard error of the sample mean decreases. }\\ \hline C&\text { The population standard deviation increases.}\\ \hline D&\text {The standard error of the sample mean increases. }\\ \hline \end{array}$

The answer of A sample of size n is selected...

The central limit theorem states that if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean \[\bar { X }\] : $\begin{array}{|l|l|} \hline A&\text { is approximately normal if \( n>30 $.}\\ \hline B&\text { is approximately normal if $ n<30 $.}\\ \hline C&\text { is approximately normal if the underlying population is normal.}\\ \hline D&\text { has the same variance as the population.}\\ \hline \end{array}\)

The answer of The central limit theorem states that if...

Exam 10: Sampling Distributions

Which of the following best describes the sampling distribution of the sample proportion? A The sampling distribution of the sample proportion is always normally distributed. B The sampling distribution of the sample proportion is approximately normally distributed provided that n p \geq 5 and nq\geq5 . C The sampling distribution of the sample proportion is skewed D None of these choices are correct.

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Question 21

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Use this information to answer the following question(s). Find the probability that a randomly selected Australian adult plays sport for more than 5 hours per day.

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Question 22

A researcher conducted a survey on a university campus for a sample of 64 third-year students and reported that third-year students read an average of 3.12 books in the prior academic semester, with a standard deviation of 2.15 books. Determine the probability that the sample mean is: a. less than 3.45. b. between 3.38 and 3.58. c. above 2.94.

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Question 23

When a great many simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size n.

(True/False)

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Question 24

A video rental store wants to know what proportion of its customers are under 21 years old. A simple random sample of 500 customers is taken, and 350 of them are under 21. Assume that the true population proportion of customers aged under 21 is 0.68. If another simple random sample of size 500 is taken, what is the probability that more than 70% of customers are under 21 years old?

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Question 25

The following table gives the number of pets owned for a population of four families. Family A B C D Number of pets owned 2 1 4 3 Find the mean and standard deviation for the population.

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Question 26

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s). What is the probability that a randomly selected woman is shorter than 162 centimetres?

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Question 27

If it is known that the population proportion of car parks in a particular city that offer early discount fees is 25%, which of the following best describes the mean and standard deviation of the sampling distribution of the sample proportion of car parks that offer early discount fees for samples taken of size 30? A The mean is 0.25 and the standard deviation is 0.006 . B The mean is 0.25 and the standard deviation is 0.75 . C The mean is 0.25 and the standard deviation is 0.079 . D None of these choices are correct.

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Question 28

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is: A. 0.4332. B. 0.0668. C. 0.0987. D. 0.9013.

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Question 29

A sample of 50 observations is drawn at random from a normal population whose mean and standard deviation are 75 and 6, respectively. a. What does the central limit theorem say about the sampling distribution of the sample mean? Why? b. Find the mean and standard error of the sampling distribution of the sample mean. c. Find P( $\bar { X }$ > 73). d. Find P( $\bar { X }$ < 74).

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Question 30

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Find the probability that if four Australian adults are randomly selected, their average number of hours spent playing sport is more than 5 hours per day.

(Short Answer)

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Question 31

A sample of size n is selected at random from an infinite population. As n increases, which of the following statements is true? A The population standard deviation decreases. B The standard error of the sample mean decreases. C The population standard deviation increases. D The standard error of the sample mean increases.

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Question 32

Suppose that the average annual income of a lawyer is $150 000 with a standard deviation of $40 000. Assume that the income distribution is normal. a. What is the probability that the average annual income of a sample of 5 lawyers is more than $120 000? b. What is the probability that the average annual income of a sample of 15 lawyers is more than $120 000?

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Question 33

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Find the probability that if four Australian adults are randomly selected, all four play sport for more than 5 hours per day.

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Question 34

If all possible samples of size n are drawn from an infinite population with a mean of 60 and a standard deviation of 8, then the standard error of the sample mean equals 1.0 only for samples of size 64.

(True/False)

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Question 35

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a variance of 100 centimetres². A random sample of five women is selected. What is the probability that the sample mean is greater than 162 centimetres?

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Question 36

A local newspaper sells an average of 2100 papers per day, with a standard deviation of 500 papers. Consider a sample of 60 days of operation. a. What is the shape of the sampling distribution of the sample mean number of papers sold per day? Why? b. Find the expected value and the standard error of the sample mean. c. What is the probability that the sample mean will be between 2000 and 2300 papers?

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Question 37

A sample of size 35 is selected at random from a finite population. If the finite population correction factor is 0.5, then (rounded to the nearest integer) the population size is: A. 46. B. 2116. C. 78. D. 35.

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Question 38

An infinite population has a mean of 120 and a standard deviation of 44. A sample of 100 observations is to be selected at random from the population. a. What is the expected value of the sample mean? b. What is the standard deviation of the sample mean? c. What is the shape of the sampling distribution of the sample mean? d. What does the sampling distribution of the sample mean show?

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Question 39

The central limit theorem states that if a random sample of size n is drawn from a population, then the sampling distribution of the sample mean $\bar { X }$ : A is approximately normal if n>30 . B is approximately normal if n<30 . C is approximately normal if the underlying population is normal. D has the same variance as the population.

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Question 40

Showing 21 - 40 of 68

When a great many simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size n.

The following table gives the number of pets owned for a population of four families. Family A B C D Number of pets owned 2 1 4 3 Find the mean and standard deviation for the population.

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s). What is the probability that a randomly selected woman is shorter than 162 centimetres?

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is: A. 0.4332. B. 0.0668. C. 0.0987. D. 0.9013.

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Find the probability that if four Australian adults are randomly selected, all four play sport for more than 5 hours per day.

If all possible samples of size n are drawn from an infinite population with a mean of 60 and a standard deviation of 8, then the standard error of the sample mean equals 1.0 only for samples of size 64.

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a variance of 100 centimetres². A random sample of five women is selected. What is the probability that the sample mean is greater than 162 centimetres?

A sample of size 35 is selected at random from a finite population. If the finite population correction factor is 0.5, then (rounded to the nearest integer) the population size is: A. 46. B. 2116. C. 78. D. 35.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

Exam 10: Sampling Distributions

When a great many simple random samples of size n are drawn from a population that is normally distributed, the sampling distribution of the sample means will be normal, regardless of sample size n.

The following table gives the number of pets owned for a population of four families. Family A B C D Number of pets owned 2 1 4 3 Find the mean and standard deviation for the population.

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. Use this information to answer the following question(s). What is the probability that a randomly selected woman is shorter than 162 centimetres?

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, exceeds 78 is: A. 0.4332. B. 0.0668. C. 0.0987. D. 0.9013.

The amount of time spent by Australian adults playing sports per day is normally distributed, with a mean of 4 hours and standard deviation of 1.25 hours. Find the probability that if four Australian adults are randomly selected, all four play sport for more than 5 hours per day.

If all possible samples of size n are drawn from an infinite population with a mean of 60 and a standard deviation of 8, then the standard error of the sample mean equals 1.0 only for samples of size 64.

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a variance of 100 centimetres2. A random sample of five women is selected. What is the probability that the sample mean is greater than 162 centimetres?

A sample of size 35 is selected at random from a finite population. If the finite population correction factor is 0.5, then (rounded to the nearest integer) the population size is: A. 46. B. 2116. C. 78. D. 35.

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Methods Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Statistical Inference: Introduction

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Inference About Population Variances

Analysis of Variance

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Model Building

Nonparametric Techniques

Statistical Inference: Conclusion

Time-Series Analysis and Forecasting

Index Numbers

Decision Analysis

Filters

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a variance of 100 centimetres². A random sample of five women is selected. What is the probability that the sample mean is greater than 162 centimetres?