Exam 11: Estimation: Describing a Single Population

The head of the statistics department in a certain university believes that 70% of the department's graduate assistantships are given to international students. A random sample of 50 graduate assistants is taken. a. Assume that the chairman is correct and p = 0.70. What is the sampling distribution of the sample proportion $\hat { p }$ . Explain. b. Find the expected value and the standard error of the sampling distribution of $\hat { p }$ . c. What is the probability that the sample proportion $\hat { p }$ will be between 0.65 and 0.73? d. What is the probability that the sample proportion $\hat { p }$ will be within ±0.05 of the population proportion p?

(Essay)

4.9/5

(39)

Question 41

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

(True/False)

4.9/5

(33)

Question 42

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

(Multiple Choice)

4.7/5

(38)

Question 43

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Determine the 95% confidence interval estimate of the population mean, changing the population standard deviation to 2.

(Essay)

4.8/5

(40)

Question 44

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use, changing the standard deviation to 90?

(Essay)

4.8/5

(38)

Question 45

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown?

(Multiple Choice)

4.7/5

(32)

Question 46

In an effort to identify the true proportion of first-year university students who are under 18 years of age, a random sample of 500 first-year students was taken. Only 50 of them were under the age of 18. The value 0.10 would be used as a point estimate to the true proportion of first-year students aged under 18.

(True/False)

4.8/5

(26)

Question 47

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use, changing the standard deviation to 50?

(Essay)

4.8/5

(35)

Question 48

Find and interpret a 95% confidence interval for the population mean number of laptops owned by an average Australian household, if a random sample of 40 Australian households had a sample mean of 1.3 laptops. The population variance is known to be 4 laptops².

(Essay)

4.9/5

(38)

Question 49

The width of a confidence interval estimate of the population mean widens when the:

(Multiple Choice)

4.7/5

(38)

Question 50

An unbiased estimator of a population parameter is an estimator whose expected value is equal to the population parameter to be estimated.

(True/False)

4.7/5

(41)

Question 51

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is:

(Multiple Choice)

4.7/5

(33)

Question 52

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

(Essay)

4.9/5

(30)

Question 53

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use with a 90% confidence level?

(Essay)

4.8/5

(40)

Question 54

As the number of degrees of freedom for a t-distribution increases:

(Multiple Choice)

4.8/5

(30)

Question 55

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .

(True/False)

4.8/5

(31)

Question 56

As a manufacturer of golf clubs, a major corporation wants to estimate the proportion of golfers who are right-handed. How many golfers must be surveyed if they want to be within 0.02 with a 95% confidence level: a. assuming that there is no information available that could be used as an estimate of p? b. assuming that the manufacturer has an estimate of p obtained from a previous study that suggests that 75% of golfers are right-handed?

(Essay)

4.9/5

(27)

Question 57

Which of the following is true about the t-distribution?

(Multiple Choice)

4.9/5

(28)

Question 58

Suppose that the amount of time teenagers spend on the Internet is normally distributed, with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean is computed as 6.5 hours. Determine the 95% confidence interval estimate of the population mean. Interpret

(Essay)

4.8/5

(42)

Question 59

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

(Essay)

4.8/5

(34)

Question 60

Showing 41 - 60 of 127

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use, changing the standard deviation to 90?

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown?

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use, changing the standard deviation to 50?

Find and interpret a 95% confidence interval for the population mean number of laptops owned by an average Australian household, if a random sample of 40 Australian households had a sample mean of 1.3 laptops. The population variance is known to be 4 laptops².

The width of a confidence interval estimate of the population mean widens when the:

An unbiased estimator of a population parameter is an estimator whose expected value is equal to the population parameter to be estimated.

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is:

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use with a 90% confidence level?

As the number of degrees of freedom for a t-distribution increases:

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .

Which of the following is true about the t-distribution?

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

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

Sampling Distributions

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 11: Estimation: Describing a Single Population

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows smaller as the sample size grows larger.

The use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p requires that:

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use, changing the standard deviation to 90?

Which of the following statistical distributions is used when estimating the population mean when the population variance is unknown?

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use, changing the standard deviation to 50?

Find and interpret a 95% confidence interval for the population mean number of laptops owned by an average Australian household, if a random sample of 40 Australian households had a sample mean of 1.3 laptops. The population variance is known to be 4 laptops2.

The width of a confidence interval estimate of the population mean widens when the:

An unbiased estimator of a population parameter is an estimator whose expected value is equal to the population parameter to be estimated.

The sample variance s2s ^ { 2 }s2 is an unbiased estimator of the population variance σ2\sigma ^ { 2 }σ2 when the denominator of s2s ^ { 2 }s2 is:

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion p^\hat { p }p^​ ? b. What is the standard error of the sample proportion p^\hat { p }p^​ ?

Suppose that your task is to estimate the mean of a normally distributed population to within 10 units with 95% confidence and that the population standard deviation is known to be 70. What sample size should you use with a 90% confidence level?

As the number of degrees of freedom for a t-distribution increases:

Suppose that a 90% confidence interval for μ\muμ is given by xˉ±0.75\bar { x } \pm 0.75xˉ±0.75 . This notation means that we are 90% confident that μ\muμ falls between xˉ−0.75\bar { x } - 0.75xˉ−0.75 and xˉ+0.75\bar { x } + 0.75xˉ+0.75 .

Which of the following is true about the t-distribution?

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

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

Sampling Distributions

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

Find and interpret a 95% confidence interval for the population mean number of laptops owned by an average Australian household, if a random sample of 40 Australian households had a sample mean of 1.3 laptops. The population variance is known to be 4 laptops².

The sample variance $s ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ when the denominator of $s ^ { 2 }$ is:

A simple random sample of 100 observations is taken from a population. Assume that the population proportion p = 0.5. a. What is the expected value of the sample proportion $\hat { p }$ ? b. What is the standard error of the sample proportion $\hat { p }$ ?

Suppose that a 90% confidence interval for $\mu$ is given by $\bar { x } \pm 0.75$ . This notation means that we are 90% confident that $\mu$ falls between $\bar { x } - 0.75$ and $\bar { x } + 0.75$ .