ECO FINAL FR
The Greensboro Convention & Visitors Bureau has determined that across all hotels in the Triad region, the price for a one-night stay follows a normal distribution with mean $143 and standard deviation $38. A new hotel in the Triad wants to offer a competitive nightly rate: only 40% of the area hotels should charge less for a room. What is the price the new hotel should charge (rounded to whole dollars)?
$134
The Greensboro Convention & Visitors Bureau has determined that across all hotels in the Triad region, the price for a one-night stay follows a normal distribution with mean $143 and standard deviation $38. What is the probability that a randomly chosen hotel charges exactly $181 per night?
0
The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the standard error of the mean?
0.0200
A study reports that only 12% of people stick to their New Year's resolutions. Suppose you sample 100 people about whether they stuck to their resolutions. What is the standard error of the proportion?
0.0325
The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the probability of obtaining a sample mean within 0.01 ounces of the population mean?
0.3085
The Greensboro Convention & Visitors Bureau has determined that across all hotels in the Triad region, the price for a one-night stay follows a normal distribution with mean $143 and standard deviation $38. What is the probability that a randomly chosen hotel charges between $120 and $190 per night?
0.622
The Greensboro Convention & Visitors Bureau has determined that across all hotels in the Triad region, the price for a one-night stay follows a normal distribution with mean $143 and standard deviation $38. What is the probability that a randomly chosen hotel charges less than $200 per night?
0.933
The age (in years) of cars currently on the road in the U.S. is normally distributed. A researcher from the firm IHS Automotive selected a random sample of 30 cars and calculated the interval [10.39, 14.03] as the 95% confidence interval for the average age. The margin of error is _____.
1.82
Suppose you randomly select a sample of 4 observations from a population with μ = 7 and σ = 2. You find a sample mean x ¯ = 9. The sampling error is _____.
2
A study reports that only 12% of people stick to their New Year's resolutions. You are considering whether to sample 100 people or 200 people to verify the results of the study. With which sample size are you more likely to find a sample proportion that is close to the population proportion?
200
When selecting, with replacement, a simple random sample of 2 observations from a population of 5 observations, the number of possible samples you can select is ____.
25
Information
Data that are transformed into useful facts that can be used for a specific purpose, such as making a decision.
Ratio Data
Data that have all the features of interval data, with that added feature of having a true zero point.
Ordinal Data
Data that have all the properties of nominal data but that also permit the rank-ordering of values from highest to lowest.
Cross-Sectional Data
Data values collected from a number of subjects during a single period of time.
Time-Series Data
Data values that correspond to a specific measurement over a range of time.
Primary Data
Data you have collected yourself.
Null Hypothesis
Designated H0, this hypothesis represents the status quo and involves stating the belief that the population is ≤, =, ≥ a specific value and is always associated with an equal sign.
Alternative Hypothesis
Designated H1, this hypothesis represents the opposite of the null hypothesis and holds true if the null hypothesis is found to be false. The alternative hypothesis always states the population parameter is <, ≠, < a specific value.
Non-Sampling Errors
Errors that occur as a result of problems such as data collection mistakes, ambiguous survey questions, and questions that lead respondents to certain "correct" answers.
Mutually Exclusive Events
Events that cannot occur at the same time.
Dependent Events
Events wherein the occurrence of one event affect the occurrence of another event.
Population Coefficient of Determination, p^2
Measures the percentage of total variation of the dependent variable that is explained by the independent variable from the population.
Combinations
Number of different ways in which objects can be arranged without regard to order.
Subjective Probability
Probability determined by the experience and intuition of a person, made when classical and empirical probabilities cannot be calculated.
Nominal Data
Qualitative data observations that are assigned to predetermined categories.
The weight of a package of Seattle's Best ground coffee is normally distributed with a standard deviation of 1.8 ounces. A production manager at the company collects a random sample of 20 packages and finds a sample mean weight of 23.6 ounces. The 95% confidence interval for the average weight of a package of coffee is _____.
[22.8, 24.4]
If we consider the simple random sampling process as an experiment, the sample mean is _____.
a random variable
In a random sample, the expected value of the sample mean is _____.
equal to the population mean
The sample mean x ¯ has an approximately normal distribution _____.
if the sample size is greater than or equal to 30
The sampling distribution of the sample mean _____.
is the sampling distribution showing all possible values of the sample mean
As a general rule, the sampling distribution of the proportion can be approximated by a normal probability distribution whenever what condition(s) hold(s)?
np>5 and n(1-p)>5
The standard deviation of the distribution of the sample mean is called the _____.
standard error of the mean
If a random variable has a standard normal distribution, _____.
the mean is 0 and the standard deviation is 1
If x is a continuous random variable, then _____.
the probability that x lies in an interval is an area under the density function
Larger values of the standard deviation result in a normal distribution curve that is _____.
wider and flatter
Suppose x is a random variable and you standardize it by calculating the z-score. A value z = -0.7 means that _____.
x lies 0.7 standard deviations below its mean
The basis for using a normal probability distribution to approximate the sampling distribution of x ¯ and p ¯ is called _____.
The Central Limit Theorem
Residual, e_i
The difference between the actual data value and the predicted value.
Expected Monetary Value (EMV)
The dollar outcome that can be expected based on a probability distribution.
Simple Probability
The likelihood of a single event occurring.
Regression Line
The line created by a regression analysis that best fits the data.
Permutations
The number of different ways in which objects can be arranged in order.
Confidence Level
The probability that the interval estimate will include the population parameter of interest, such as the mean or the proportion.
Census
The process of recording information from an entire population.
Right-Skewed Distribution
The shape of the distribution when its mean is higher than its median.
Left-Skewed Distribution
The shape of the distribution when the median is larger than the mean.
What happens as the sample size increases?
The standard error of the mean decreases.
Margin of Error
The width of the confidence interval between a sample mean or a proportion and its upper limit and or its lower limit.
Normal Probability Pilot
Used to verify if data follow the normal probability distribution by graphing the data on the y-axis and the z-scores for the data on the x-axis.
Bootstrap Method
Using computer software to extract many samples with replacement in order to estimate a parameter of the population.
Discrete Data
Values based on observations that can be counted; they are restricted to integer values (whole numbers).
Statistics
Values calculated from a sample, such as the mean or median.
Outliers
Values that are much higher or lower than most of the data.
Continuous Data
Values that can take on any real numbers, including numbers that contain decimal points.
Parameters
Values that describe some characteristic of a population, such as the mean or the median.
A population consists of 3 numbers: 2, 10 and 6. You randomly select a sample of 2 observations without replacement and calculate the sample mean. The expected value of the sample mean is _____.
6
A population consists of 3 numbers: 2, 10 and 6. You randomly select a sample of 2 observations without replacement and calculate the sample mean. The variance of the sample mean is _____.
8/3
Producer's Risk
A Type I error that occurs in quality control settings, because the producer is looking for a problem in its process that does not exist.
Consumer's Risk
A Type II error when it occurs in quality control settings, because the consumer is getting a product from a process that is not performing properly.
Class
A category in a frequency distribution.
Sample Correlation Coefficient
A coefficient that indicates both the strength and direction of a linear relationship between independent and dependent variables from a sample.
Sample Coefficient of Determination, R^2
A coefficient that measures the percentage of the total variation of a dependent variable that is explained by an independent variable.
Population Correlation Coefficient, p
A coefficient that refers to the correlation between all values of two variables of interest in a population.
Least Squares Method
A mathematical procedure used to identify the linear equation that best fits a set of ordered pairs. The procedure involves finding values for b0, the y-intercept, and b1, the slope.
Z-Score
A measure that identifies the number of standard deviations a value is from the mean of the distribution.
Periodicity
A pattern in the population that is consistent with the value of k in systematic sampling.
Empirical Probability
A probability determined by counting the frequency of an event during an experiment.
Hypergeometric Distribution
A probability distribution that occurs when samples are randomly selected from a finite population without being replaced. Under these conditions, the probabilities of success change repeatedly because the sample space becomes smaller and smaller after each selection.
Classical Probability
A probability that is determined by dividing the number of possible outcomes of an event by the total number of possible outcomes in the sample space.
Homoscedasticity
A regression assumption that states that the variation of a dependent variable is the same across all values of an independent variable.
Empirical Rule
A rule that states that approximately 68%, 95% and 99.7% of a distribution's data values will fall within one, two, and three standard deviations above and below the mean, respectively, if the distribution is symmetrical and bell shaped.
Probability Sample
A sample in which each member in population has a known, nonzero chance of being selected for the sample.
Systematic Sample
A sample in which every kth member of the population is chosen, with the value k being equal to N/n.
Non-probability Sample
A sample in which the probability of a population member being selected for the sample is not known.
Which of the following is true for a point estimate?
A sample statistic is a point estimate of a population parameter.
Biased Sample
A sample that does not represent the intended population and that can lead to distorted findings.
Point Estimate
A single value that best describes the population of interest, with the sample mean and sample proportion being the most common.
Central Tendency
A single value used to describe the center point of a data set.
Linear Chart
A special type of scatter plot in which the data points in the scatter point are connected with a line.
Correlation Coefficient
A statistic that measures the strength and direction of the linear relationship between two variables.
Resampling
A statistical technique where many samples are repeatedly drawn from a population.
Frequency Distribution
A table that shows the number of data observations that fall into specific intervals.
Simple Regression Analysis
A technique that allows us to describe a straight line that best fits a series of ordered pairs (x,y).
Standard Error of the Slope, s_b
A value that measures how consistent the slope of a regression equation, b, would be if several sets of samples from the population were selected and the regression equation were derived from each of them.
Standard Error of the Estimate, s_e
A value that measures the amount of dispersion of observed data around a regression line.
Sum of Squares Regression (SSR)
A value that measures the amount of variation in a dependent variable that is explained by an independent variable.
Sum of Squares Error (SSE)
A value that measures the variation in a dependent variable that is explained by variables other than an independent variable.
Total Sum of Squares
A value that measures the variation in the values of a dependent variable.
Independent Variable
A variable that explains the variation in the dependent variable, y.
Dependent Variable
A variable that is explained by the independent variable, x.
Alpha (α)
A variable that represents the probability that any given confidence interval will not contain the true population mean or proportion. (Also known as the significance level).
Which of the following applies to random sampling?
All observations in the population are equally likely to be selected into the sample.
Hypothesis
An assumption about a population parameter such as a mean or a proportion.
Type II Error
An error that occurs when the null hypothesis is not rejected when, in reality, it is not true. The probability of making a Type II error is known as β.
Type I Error
An error that occurs when the null hypothesis is rejected when, in reality, it is true. The probability of making a Type I error is known as α, the level of significance.
Poisson Process
An experiment with the following characteristics: (1) The experiment involves counting the number of occurrences of an event over a period of time, area, distance, or any other type of measurement; (2) the mean of the distribution has to be the same for each interval of measurement; (3) the number of occurrences during one interval is independent of the number of occurrences in any other interval.
Which of the following is true for a convenience sample?
Groups of observations are sampled simultaneously
Continuous Random Variables
Have outcomes that take on any numerical value, including fractions, as a result of conducting an experiment.
Discrete Random Variables
Have outcomes that take on whole numbers as a result of conducting an experiment.
