ECON TEST 2 QUIZLET
Under what condition is the finite population correction factor used for computing the standard error of X¯ and P¯ ? n ≥ Np n < Np n ≥ 0.05N n < 0.05N
n ≥ 0.05N
Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?
A larger sample size reduces the margin of error.
Which of the following meets the requirements of a cluster sample? A population can be divided into 50 city blocks. The sample will include one hundred people who volunteer for the sample from any city block. A population can be divided into 50 city blocks. The sample will include one hundred people chosen at random, without regard to the city block where they live. A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks. A population can be divided into 50 city blocks. The sample will include two people chosen at random from each city block.
A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks.
If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?
For any sample size n, the sampling distribution of the sample mean is normally distributed.
For a given sample size and population standard deviation, which of the following is true in the interval estimation of the population mean?
If the confidence level is greater, the interval is wider.
When the required sample size calculated by using a formula and not a whole number, what is the best choice for the required sample size?
Round the result of the calculation to the nearest whole number.
Which of the following is the necessary condition for creating confidence intervals for the population mean? Normality of the estimator Normality of the population Known population parameter Known standard deviation of the estimator
Normality of the estimator
It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X < 20) related to P(X < 16)?
P(X < 20) is greater than P(X < 16).
Which of the following does not represent a continuous random variable?
The number of customer arrivals to a bank between 10 am and 11 am.
Which of the following statements is FALSE regarding the given curves showing the shapes of a probability density function for different values of a key parameter λ?
The red curve has the lowest value of the rate parameter λ.
Bias can occur in sampling. Bias refers to _______.
The tendency of a sample statistic to systematically over or underestimate a population parameter.
Nonresponse bias occurs when
Those responding to a survey or poll differ systematically from the non-respondents
The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval? n≥30n ≥ 30 np⎯⎯≥5n p¯ ≥ 5 np≥ 5 and n( 1 − p¯) ≥ 5 np≥5np ≥ 5 and n(1−p)≥5
np≥ 5 and n( 1 − p¯) ≥ 5
What is the most typical form of a calculated confidence interval?
point estimate +- margin of error
Selection bias occurs when:
portions of the population are excluded from the consideration for the sample
For a categorical variable, the most appropriate control chart to monitor the proportion of a certain characteristic is a(n) p¯ chart. x¯ chart. c chart. s chart.
p¯ chart.
As sample size increases
standard error of the mean decreases
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then __________. the resulting margin of error will increase and the risk of reporting an incorrect interval will increase the resulting margin of error will decrease and the risk of reporting an incorrect interval will increase the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease the resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease
the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been _________. wider; bigger wider; smaller narrower; bigger narrower; smaller
wider; smaller
For a numerical variable, the most appropriate control chart to monitor central tendency is a(n) p¯ chart x¯ chart. c chart. s chart.
x¯ chart.
A random sample of 120 cast aluminum pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.05. What are the upper and lower control limits for the p⎯⎯p¯ chart?
0.1097 and 0.0
The probability that a normal random variable is less than its mean is:
0.5
Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate p^ of the population proportion, what value should be assumed for p^ ? 0.05 0.10 0.50 0.90
0.50
What is the z score for a 90% confidence interval of population mean?
1.645
If an exponential distribution has the rate parameter λ = 5, what is its expected value? 5 1/5 1/25 5/2
1/5
Sixty percent of 800 students in a Business Statistics class are female. If you want to make probability estimates of the sample proportion of female students without applying the finite population correction factor, what minimal sample size of the random sample should be used?
40
The finite population correction factor for the standard error of the mean should be used when the ratio of the sample size to the size of population exceeds ______. 1% 2% 3% 5%
5%
Sarah's portfolio has an expected annual return at 8%, with an annual standard deviation at 12%. If her investment returns are normally distributed, then in any given year Sarah has an approximate ______. 50% chance that the actual return will be greater than 8% 68% chance that the actual return will fall within 4% and 20% 68% chance that the actual return will fall within −20% and 20% Incorrect 95% chance that the actual return will fall within −4% and 28%
50% chance that the actual return will be greater than 8%
Which of the following meets the requirements of a simple random sample? A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age.
Which of the following meets the requirements of a stratified random sample? A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.
A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.
For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known? If the sample standard deviation is smaller, the interval is wider. If the population standard deviation is greater, the interval is wider. If the population standard deviation is smaller, the interval is wider. If the population standard deviation is greater, the interval is narrower.
If the population standard deviation is greater, the interval is wider.
For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean?
If the sample size gets bigger, the interval is narrower.
John would like to conduct a survey in his neighborhood to get homeowners' opinion on the Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample? John randomly chooses three streets and selects every third house on those streets. John selects the first 25 homes that he passes as he walks into the entrance of the development. John selects every third house on each street. John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group.
John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group.
Peggy would like to conduct a survey in her neighborhood to get homeowners' opinions on the Delmarva proposal to switch to natural gas. Which of the following is an example of a convenience sample? John randomly chooses three streets and selects every third house on those streets. John selects the first 25 homes that he passes as he walks into the entrance of the development. John selects every third house on each street. John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group.
John selects the first 25 homes that he passes as he walks into the entrance of the development.
The finite correction factor is always ______. less than one, and therefore increases the standard deviations of X⎯⎯⎯X¯ and P⎯⎯⎯P¯ computed under the assumption of infinite population less than one, and therefore decreases the standard deviations of X⎯⎯⎯X¯ and P⎯⎯⎯P¯ computed under the assumption of infinite population greater than one, and therefore increases the standard deviations of X⎯⎯⎯X¯ and P⎯⎯⎯P¯ computed under the assumption of infinite population greater than one, and therefore decreases the standard deviations of X⎯⎯⎯X¯ and P⎯⎯⎯P¯ computed under the assumption of infinite population
Less than one, and therefore decreases the standard deviations of and assumption of infinite population computed under the
What is the purpose of calculating a confidence interval? To provide a range of values that has a certain large probability of containing the sample statistic of interest. To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest. To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest. To provide a range of values that has a certain large probability of containing the population parameter of interest.
To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.
Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $22.31 and a 95% confidence interval of [$20.5051, $24.2091]. Which of the following statements is a valid explanation of the confidence interval. 95% of all taxi fares are between $20.51 and $24.21. We are 95% confident that a randomly selected taxi fare will be between $20.51 and $24.21. The mean amount of a taxi fare is $22.31, 95% of the time. We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.
We are 95% confident that the average taxi fare between Logan Airport and downtown Boston will fall between $20.51 and $24.21.
A random sample of 150 cast aluminum pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.04. The sample proportions for the week are shown in the accompanying table. Is the production process in control?
Yes, because the sample proportions fall within the upper and lower control limits
In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to ______. the variation caused by stratified random sampling the variation caused by the use of the finite correction factor specific events or factors that can usually be identified and eliminated a number of randomly occurring events that are part of the production process
a number of randomly occurring events that are part of the production process
Acceptance sampling is _______. a division of the population into strata a plot of calculated statistics of the production process over time an inspection of a portion of the products at the completion of the production process a determination of a point at which the production process does not conform to specifications
an inspection of a portion of the products at the completion of the production process
The detection approach to statistical quality control ______. divides the population into strata inspects a portion of the products at the completion of the production process determines at which point the production process does not conform to specifications uses the finite correction factor when the sample size is not much smaller than the population size
determines at which point the production process does not conform to specifications
Which of the following is not a characteristic of a probability density function f(x)? f(x) ≥ 0 for all values of x. f(x) is symmetric around the mean. Correct The area under f(x) over all values of x equals one. f(x) becomes zero or approaches zero if x increases to +infinity or decreases to −infinity.
f(x) is symmetric around the mean.