Question 1

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

Accepted Answer

A) Student t distribution 
B) Standard normal distribution 
C) Chi-square distribution 
D) None of these choices are correct. 
A) Student t distribution 
B) Standard normal distribution 
C) Chi-square distribution 
D) None of these choices are correct.

Question 2

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:

Accepted Answer

A) 0.0274. 
B) 0.50. 
C) 0.0316. 
D) 0.0548. 
A) 0.0274. 
B) 0.50. 
C) 0.0316. 
D) 0.0548.

Question 3

A sample of 50 students was asked how much time they spend on average a week in front of a computer. The sample mean and sample standard deviation were 15.8 and 2.7 hours, respectively. Estimate with 95% confidence interval the mean number of hours students spend in front of a computer a week.

Accepted Answer

The answer of A sample of 50 students was asked...

Question 4

The sample variance s2 is an unbiased estimator of the population variance F1F1F1S1F1F1F102 when the denominator of s2 is: $\begin{array}{|l|l|}
\hline\text { A. } & n \
\hline \text { B. } & n-1 \
\hline \text { C. } & \sqrt{n} \
\hline \text { D. } & n+1 \
\hline
\end{array}$

Accepted Answer

The answer of The sample variance s2 is an unbiased...

Question 5

In the formula $$\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$$ , the ?/2 refers to:

Accepted Answer

A) the probability that the confidence interval will contain the population mean. 
B) the probability that the confidence interval will not contain the population mean. 
C) the area in the lower tail or upper tail of the sampling distribution of the sample mean. 
D) the level of confidence. 
A) the probability that the confidence interval will contain the population mean. 
B) the probability that the confidence interval will not contain the population mean. 
C) the area in the lower tail or upper tail of the sampling distribution of the sample mean. 
D) the level of confidence.

Question 6

The student t-distribution approaches the normal distribution as the:

Accepted Answer

A) number of degrees of freedom increases. 
B) number of degrees of freedom decreases. 
C) sample size decreases. 
D) population size increases. 
A) number of degrees of freedom increases. 
B) number of degrees of freedom decreases. 
C) sample size decreases. 
D) population size increases.

Question 7

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?

Accepted Answer

The answer of Suppose that your task is to estimate...

Question 8

The mean of the sampling distribution of the sample proportion $\hat { p }$ , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

Accepted Answer

A) True 
 B)False

Question 9

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

Accepted Answer

A) True 
 B)False

Question 10

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

Accepted Answer

A) 77.769. 
B) 72.231. 
C) 72.727. 
D) 77.273. 
A) 77.769. 
B) 72.231. 
C) 72.727. 
D) 77.273.

Question 11

The upper limit of the 90% confidence interval for µ, given that n = 64, $$\bar { X }$$ = 70 and F1F1F1S1?F1F1F10 = 20, is 65.89.

Accepted Answer

A) True 
 B)False

Question 12

A politician believes that the proportion of voters who will vote for a Coalition candidate in the 2004 general election is 0.65. A sample of 500 voters is selected at random.
a. Assume that the politician is correct and p = 0.65. What is the sampling distribution of the sample proportion $\hat { p }$ ? Explain.
b. Find the expected value and standard deviation of the sample proportion $\hat { p }$ .
c. What is the probability that the number of voters in the sample who will vote for a Labor candidate in the 2004 general election will be between 340 and 350?

Accepted Answer

a. Approximately normal, since

Question 13

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.

Accepted Answer

A) True 
 B)False

Question 14

A random sample of 10 waitresses in Darwin revealed the following hourly earnings (in dollars, including tips): $\begin{array}{|r|r|r|r|r|r|r|r|r|r|}
\hline19&18&15&16&18&17&16&18&20&14\
\hline
\end{array}$ If the hourly earnings are normally distributed with a standard deviation of $4.5, estimate with 95% confidence the mean hourly earnings for all waitresses in Darwin.

Accepted Answer

$14.3109 t

Question 15

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?

Accepted Answer

a. Approximately normal, since

Question 16

In developing an interval estimate for a population mean, the interval estimate was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was:

Accepted Answer

A) 56.34. 
B) 62.96. 
C) 13.24. 
D) 66.15. 
A) 56.34. 
B) 62.96. 
C) 13.24. 
D) 66.15.

Question 17

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

Accepted Answer

The answer of How large a sample should be taken...

Question 18

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $$\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )$$

Accepted Answer

A) The sample size is greater than 30. 
B) The population variance is known. 
C) The population is normal. 
D) The sample is drawn from a positively skewed distribution. 
A) The sample size is greater than 30. 
B) The population variance is known. 
C) The population is normal. 
D) The sample is drawn from a positively skewed distribution.

Question 19

After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be:

Accepted Answer

A) 800. 
B) 200. 
C) 4000. 
D) 1600. 
A) 800. 
B) 200. 
C) 4000. 
D) 1600.

Question 20

A 95% confidence interval estimate for a population mean F1F1F1S1F1F1F10 is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence intervalF1F1F1S1F1F1F10:

Accepted Answer

A) becomes wider. 
B) remains the same. 
C) becomes narrower. 
D) None of these choices are correct. 
A) becomes wider. 
B) remains the same. 
C) becomes narrower. 
D) None of these choices are correct.

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

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:

A sample of 50 students was asked how much time they spend on average a week in front of a computer. The sample mean and sample standard deviation were 15.8 and 2.7 hours, respectively. Estimate with 95% confidence interval the mean number of hours students spend in front of a computer a week.

The sample variance s2 is an unbiased estimator of the population variance 2 when the denominator of s2 is: A. n B. n-1 C. D. n+1

In the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ , the ?/2 refers to:

The student t-distribution approaches the normal distribution as the:

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?

The mean of the sampling distribution of the sample proportion $\hat { p }$ , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

The upper limit of the 90% confidence interval for µ, given that n = 64, $\bar { X }$ = 70 and ? = 20, is 65.89.

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.

In developing an interval estimate for a population mean, the interval estimate was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was:

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )$

After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be:

A 95% confidence interval estimate for a population mean  is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval:

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

Statistical Inference and Sampling Distributions

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

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Exam 10: Estimation: Describing a Single Population

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

A sample of 250 observations is to be selected at random from an infinite population. Given that the population proportion is 0.25, the standard error of the sampling distribution of the sample proportion is:

A sample of 50 students was asked how much time they spend on average a week in front of a computer. The sample mean and sample standard deviation were 15.8 and 2.7 hours, respectively. Estimate with 95% confidence interval the mean number of hours students spend in front of a computer a week.

The sample variance s2 is an unbiased estimator of the population variance 2 when the denominator of s2 is: A. n B. n-1 C. D. n+1

In the formula Xˉ±za/2(σ/n)\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )Xˉ±za/2​(σ/n​) , the ?/2 refers to:

The student t-distribution approaches the normal distribution as the:

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?

The mean of the sampling distribution of the sample proportion p^\hat { p }p^​ , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

It is possible to construct a confidence interval estimate of the population mean if the population variance is unknown.

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25. The upper limit of a 95% confidence interval for the population mean would equal:

The upper limit of the 90% confidence interval for µ, given that n = 64, Xˉ\bar { X }Xˉ = 70 and ? = 20, is 65.89.

A confidence interval becomes narrower as the sample size increases, for the same percentage of confidence.

In developing an interval estimate for a population mean, the interval estimate was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was:

How large a sample should be taken to estimate a population proportion to within 0.01 with 90% confidence if the proportion is known to be around 5%?

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? Xˉ±tan,n−1(s/n)\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )Xˉ±tan,n−1​(s/n​)

After you calculate the sample size needed to estimate a population proportion to within 0.05, your statistics lecturer tells you the maximum allowable error must be reduced to just 0.025. If the original calculation led to a sample size of 400, the sample size will now have to be:

A 95% confidence interval estimate for a population mean  is determined to be 43.78 to 52.19. If the confidence level is decreased to 90%, the confidence interval:

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

Statistical Inference and Sampling Distributions

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

In the formula $\bar { X } \pm z _ { a/2 } ( \sigma / \sqrt { n } )$ , the ?/2 refers to:

The mean of the sampling distribution of the sample proportion $\hat { p }$ , when the sample size n = 100 and the population proportion p = 0.92, is 92.0.

The upper limit of the 90% confidence interval for µ, given that n = 64, $\bar { X }$ = 70 and ? = 20, is 65.89.

In constructing a confidence interval for the population mean when the population variance is unknown, which of the following assumptions is required when using the following formula? $\bar { X } \pm t _ { a n , n - 1 } ( s / \sqrt { n } )$