Exam 9: Statistical Inference and Sampling Distributions

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:

Free

(Multiple Choice)

4.7/5

(47)

Question 1

Correct Answer:

Verified

The sampling distribution of the sample proportion is approximately normal provided that np ≥ 5 and nq ≥ 5

Free

(True/False)

4.8/5

(34)

Question 2

Correct Answer:

Verified

True

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?

Free

(Short Answer)

4.8/5

(38)

Question 3

Correct Answer:

Verified

a. 0.9535
b. 0.9981

Which of the following best describes the sampling distribution of the sample proportion?

(Multiple Choice)

4.8/5

(43)

Question 4

The objective of statistical inference is to use a sample statistic to draw conclusions about a population parameter of interest.

(True/False)

4.9/5

(34)

Question 5

In a given year, the average annual salary of an Rugby player was $205 000, with a standard deviation of $24 500. If a simple random sample of 50 players is taken, what is the probability that the sample mean will be less than $210 000?

(Short Answer)

4.8/5

(39)

Question 6

The purpose behind the statistical technique is irrelevant in statistical inference.

(True/False)

4.9/5

(31)

Question 7

Which of the following are factors that determine which statistical technique should be used?

(Multiple Choice)

4.7/5

(35)

Question 8

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

(Short Answer)

4.8/5

(27)

Question 9

The how, when and why of statistical inference puts the problem into context.

(True/False)

5.0/5

(26)

Question 10

An infinite population has a mean of 33 and a standard deviation of 6. A sample of 100 observations is to be taken at random from this population. The probability that the sample mean will be between 34.5 and 36.1 is:

(Multiple Choice)

4.9/5

(34)

Question 11

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

(True/False)

4.7/5

(34)

Question 12

The heights of women in Australia are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. If the population of women's heights were not normally distributed, which, if any, of the following questions could you answer? a. What is the probability that a randomly selected woman is taller than 160 cm? b. A random sample of five women is selected. What is the probability that the sample mean is greater than 160 cm? c. What is the probability that the mean height of a random sample of 75 women is greater than 160 cm?

(Essay)

4.8/5

(32)

Question 13

The central limit theorem is basic to the concept of statistical inference, because it permits us to draw conclusions about the population based strictly on sample data, and without having any knowledge about the distribution of the underlying population.

(True/False)

4.8/5

(31)

Question 14

It is known that 40% of voters in a certain electorate are in favour of a particular candidate. If a sample of size 30 is taken, what is the probability that less than 35% are in favour of this political candidate?

(Multiple Choice)

4.8/5

(34)

Question 15

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. Describe the sampling distribution of proportion of customers who are under age 21.

(Essay)

4.8/5

(34)

Question 16

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.

(Short Answer)

5.0/5

(34)

Question 17

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)

4.9/5

(32)

Question 18

A sample of size n is selected at random from an infinite population. As n increases the standard error of the sample mean decreases.

(True/False)

4.9/5

(42)

Question 19

A manufacturing company is concerned about the number of defective items produced by their assembly line. In the past they have had 5% of their products produced defectively. They take a random sample of 35 products. What is the probability that more than 5 products in the sample are defective?

(Multiple Choice)

4.7/5

(37)

Question 20

Showing 1 - 20 of 69

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:

The sampling distribution of the sample proportion is approximately normal provided that np ≥ 5 and nq ≥ 5

Which of the following best describes the sampling distribution of the sample proportion?

The objective of statistical inference is to use a sample statistic to draw conclusions about a population parameter of interest.

In a given year, the average annual salary of an Rugby player was $205 000, with a standard deviation of $24 500. If a simple random sample of 50 players is taken, what is the probability that the sample mean will be less than $210 000?

The purpose behind the statistical technique is irrelevant in statistical inference.

Which of the following are factors that determine which statistical technique should be used?

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

The how, when and why of statistical inference puts the problem into context.

An infinite population has a mean of 33 and a standard deviation of 6. A sample of 100 observations is to be taken at random from this population. The probability that the sample mean will be between 34.5 and 36.1 is:

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.

The central limit theorem is basic to the concept of statistical inference, because it permits us to draw conclusions about the population based strictly on sample data, and without having any knowledge about the distribution of the underlying population.

It is known that 40% of voters in a certain electorate are in favour of a particular candidate. If a sample of size 30 is taken, what is the probability that less than 35% are in favour of this political candidate?

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.

A sample of size n is selected at random from an infinite population. As n increases the standard error of the sample mean decreases.

A manufacturing company is concerned about the number of defective items produced by their assembly line. In the past they have had 5% of their products produced defectively. They take a random sample of 35 products. What is the probability that more than 5 products in the sample are defective?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

Exam 9: Statistical Inference and Sampling Distributions

Random samples of size 81 are taken from an infinite population whose mean and standard deviation are 45 and 9, respectively. The mean and standard error of the sampling distribution of the sample mean are:

The sampling distribution of the sample proportion is approximately normal provided that np ≥ 5 and nq ≥ 5

Which of the following best describes the sampling distribution of the sample proportion?

The objective of statistical inference is to use a sample statistic to draw conclusions about a population parameter of interest.

In a given year, the average annual salary of an Rugby player was $205 000, with a standard deviation of $24 500. If a simple random sample of 50 players is taken, what is the probability that the sample mean will be less than $210 000?

The purpose behind the statistical technique is irrelevant in statistical inference.

Which of the following are factors that determine which statistical technique should be used?

Assume that the time needed by a worker to perform a maintenance operation is normally distributed, with a mean of 60 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform the maintenance is between 63 and 68 minutes?

The how, when and why of statistical inference puts the problem into context.

An infinite population has a mean of 33 and a standard deviation of 6. A sample of 100 observations is to be taken at random from this population. The probability that the sample mean will be between 34.5 and 36.1 is:

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean Xˉ\bar { X }Xˉ is referred to as the normal distribution.

The central limit theorem is basic to the concept of statistical inference, because it permits us to draw conclusions about the population based strictly on sample data, and without having any knowledge about the distribution of the underlying population.

It is known that 40% of voters in a certain electorate are in favour of a particular candidate. If a sample of size 30 is taken, what is the probability that less than 35% are in favour of this political candidate?

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.

A sample of size n is selected at random from an infinite population. As n increases the standard error of the sample mean decreases.

A manufacturing company is concerned about the number of defective items produced by their assembly line. In the past they have had 5% of their products produced defectively. They take a random sample of 35 products. What is the probability that more than 5 products in the sample are defective?

What Is Statistics

Types of Data, Data Collection and Sampling

Graphical Descriptive Techniques Nominal Data

Graphical Descriptive Techniques Numerical Data

Numerical Descriptive Measures

Probability

Random Variables and Discrete Probability Distributions

Continuous Probability Distributions

Estimation: Describing a Single Population

Estimation: Comparing Two Populations

Hypothesis Testing: Describing a Single Population

Hypothesis Testing: Comparing Two Populations

Additional Tests for Nominal Data: Chi-Squared Tests

Simple Linear Regression and Correlation

Multiple Regression

Time-Series Analysis and Forecasting

Index Numbers

Filters

If all possible samples of size n are drawn from a population, the probability distribution of the sample mean $\bar { X }$ is referred to as the normal distribution.