ECO 251 Exam 3
When the relationship between the variables is statistically significant using simple regression analysis, we have enough evidence to state that the independent variable caused the change in the dependent variable.
false
A 100% confidence interval is more accurate than a 90% confidence interval and is therefore more preferable.
false
A benefit of point estimates is that they provide information about their accuracy.
false
A correlation coefficient of -0.80 is an indication of a weak negative relationship between two variables.
false
A dependent variable, x, explains the variation in another variable, which is called the independent variable, y.
false
A horizontal slope on an xy scatter plot indicates that there is a strong relationship between the between the independent and dependent variables.
false
A sample proportion equal to 0.50 will require the smallest sample size to achieve a particular margin of error for a confidence interval for the proportion.
false
A wider the margin of error will result in a more precise confidence interval.
false
All else being equal, a 90% confidence interval will be wider than a 95% confidence interval.
false
Consider the relationship between the following variables: ∙ Monthly electricity bill for a household during the summer ∙ Average high ambient temperature during the summer months Average high ambient temperature during the summer months would be considered the dependent variable.
false
Five random samples, each of size 40, are selected from a population of interest. A 90% confidence interval using a z-score is calculated for each sample. The margin of error for each confidence interval need not be the same.
false
Given a regression equation of y=15.6-3.8x , a one-unit increase in the independent variable would result in an average increase of 3.8 for the dependent variable.
false
Given that a 95% confidence interval is (6.5, 12.5), we can state that there is a 95% probability that the true population mean is between 6.5 and 12.5.
false
If the slope of the simple regression equation is equal to zero, the scatter plot for the ordered pairs will be a vertical straight line indicating that there is no relationship between the independent and dependent variables.
false
If two variables have a correlation coefficient equal to -0.60 from a sample size of 5, we can conclude that the population correlation coefficient is less than zero using α = 0.05.
false
The binomial distribution can be approximated by the Student's t-distribution when the following conditions are met: np >/= 5 and n(1-p) >/= 5 .
false
The confidence interval for the mean is symmetrical around the population mean.
false
When the sample size is more than 30 and sigma is known, the population must be normally distributed to calculate a confidence interval.
false
When the slope of a population regression line equals zero, we conclude that there is a linear relationship between the dependent and independent variables.
false
The confidence interval for the proportion is a point estimate around the sample proportion that provides us with a value for the true population proportion.
false
The correlation coefficient is a measure of the slope of the scatter plot for the independent and dependent variables.
false
The degrees of freedom are used to determine the critical z-score for the normal distribution when calculating a confidence interval.
false
The finite population correction factor for adjusting the confidence interval when sampling from a finite population is used when n/N < 0.05 .
false
The margin of error can be reduced by reducing the size of the sample.
false
The margin of error for a sample is dependent on the sample mean.
false
The necessary sample size to determine the confidence interval for the mean will double when the required margin of error is reduced by half.
false
The shape of the t-distribution becomes similar to the binomial distribution as the sample size increases.
false
When determining the sample size required for a 95% confidence interval for the population mean, the sample mean needs to be known.
false
A 99% confidence interval has a greater chance of "catching" the true population mean when compared to a 90% confidence interval.
true
A coefficient of determination equal to zero indicates that there is no relationship between the independent and dependent variables.
true
A relationship is linear if the scatter plot of the independent and dependent variables has a straight-line pattern.
true
A scatter plot is a useful tool to examine the data before conducting correlation analysis.
true
A smaller standard error of the slope increases the likelihood that we can establish a significant relationship between the independent and dependent variables.
true
An assumption of regression analysis is that the relationship between the independent and dependent variables is linear.
true
An ordered pair is a set of x and y values that pertain to a specific observation.
true
Consider the relationship between the following variables: - household income - sq. footage of the primary residence Household income would be considered the independent variable.
true
If a pilot sample is not available, it is recommended to set the sample proportion equal to 0.50 to calculate the required sample size for a confidence interval for the proportion.
true
If two variables have a correlation coefficient equal to +0.75, the scatter plot will have an upward slope moving from left to right.
true
Increasing the sample size will reduce the margin of error for a given confidence level.
true
The confidence level is a complement to the significance level.
true
The definition of a 90% confidence interval is that we expect that close to 90% of a large number of sample means drawn from a population will produce confidence intervals that include that population's mean.
true
The degrees of freedom are the number of values that are free to vary given that certain information, such as the sample mean, is known.
true
The hypothesis tests for the correlation coefficient, and the coefficient of determination will always produce the same conclusions.
true
The least squares method is a mathematical procedure used to identify the linear equation that best fits a set of ordered pairs.
true
The point estimate for the population mean will always be found within the limits of the confidence interval for the mean.
true
The point estimate may not equal the true population mean because of the presence of sampling error.
true
The purpose of generating a confidence interval for the mean is to provide an estimate for the value of the population mean.
true
The slope value for a regression equation represents the average change in the dependent variable for a one-unit increase in the independent variable.
true
The standard error of the proportion measures the average variation around the mean of the sample proportions taken from the population.
true
The total sum of squares can never be negative.
true
The values of the correlation coefficient range between -1.0 and +1.0.
true
The variation in sample means is measured by the standard error of the mean.
true
There is no guarantee that every confidence interval taken from a population will include the population mean.
true
Using the regression equation to predict values for the dependent variable beyond the range of the data may provide results that are unreliable.
true
We can approximate the standard error of the proportion by substituting the sample proportion, p, for the population proportion, p.
true
When substituting the sample standard deviation for the population standard deviation, we can no longer rely on the normal distribution to provide the critical z-score for the confidence interval.
true
When the population standard deviation is unknown, we substitute the sample standard deviation in its place to calculate confidence intervals.
true
When we use the t-distribution to calculate a confidence interval, we need to assume that the population of interest follows the normal probability distribution.
true
Without the finite population correction factor, the standard error is overestimated when calculating a confidence interval for a finite population.
true
An assumption of regression analysis is homoscedasticity, which states that the
A. variation of the dependent variable is the same across all values for the independent variable
A ________ is defined as the probability that the interval estimate will include the population parameter of interest, such as a mean or a proportion.
B. confidence level
A correlation analysis requires that the data be either ________ data or _______ data.
B. interval, ratio
A ________ is a single value that best describes the population of interest.
B. point estimate
The ________ is used to test the significance of the population correlation coefficient.
B. student's t-distribution
The critical z-score for a 98% confidence level is ________.
C. 2.33
The technique of ________ enables us to describe a straight line that best fits a series of ordered pairs (x,y).
C. simple regression analysis
The ________ measures the variation in the dependent variable that is explained by the independent variable in simple regression analysis.
C. sum of squares regression
The formula for the equation describing a straight line is y=b0+b1x. The value for b0 in this equation represents the ________________________________.
C. y-intercept of the straight line
A ________ for the mean is an interval estimate around a sample mean that provides us with a range of where the true population mean lies.
D. confidence level
The ________ indicates both the strength and direction of the linear relationship between the independent and dependent variables.
D. correlation coefficient
The formula for the equation describing a straight line is y=b0+b1x . The value for b1 in this equation represents the _______________________________.
D. slope of the straight line
The ________ measures the total variation in the dependent variable in simple regression analysis.
D. total sum of squares