BA 260 Exam 2
The least squares regression line minimizes the sum of the _____.
squared difference between actual and predicted y values
The process of making estimates and drawing conclusions about one or more characteristics of a population through analysis of sample data drawn from the population is known as _______.
statistical inference
the graph of the simple linear regression equation is an ______.
straight line
The _____ is a measure of the error that results from the estimated regression equation to predict the values of the dependent variable in the sample.
sum of squares due to error (SSE)
a procedure for using sample data to find the estimated regression equation is _____.
the least squares method
When the expected value of the point estimator is equal to the population parameter it estimates, it is said to be _____.
unbiased
The random numbers generated using Excel's RAND function follows a ____ probability distribution between 0 and 1.
uniform
A pizza shop advertises that they deliver in 30 minutes or less or its free. People who Iive in homes that are located on the opposite side of town believe that it will take the pizza shop longer than 30 minutes to make and deliver the pizza. A random sample of 50 deliveries to homes across town was taken and the mean time was computed to be 32 minutes. What is the appropriate symbol to represent the value 32?
x̄ = 32
In the graph of the simple linear regression equation, the parameter B0 represents the ________ of the true regression line.
y intercept
When the mean value of the dependent variable is independent of variation in the independent variable, the slope of the regression line is _____.
zero
A parameter is a numerical measure from a population, such as
μ
In interval estimation, as the sample size becomes larger, the interval estimate _____.
becomes narrower
As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution ____.
becomes smaller
Using an n=0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion ______.
becomes wider
The _____ is a measure of the goodness of fit the estimated regression equation. It can be interpreted as the proportion of the variability in the dependent variable y that is explained by the estimated regression equation.
coefficient of determination
The _____ is an indication of how frequently interval estimates based on samples of the same size taken from the same population using identical sampling techniques will contain the true value of the parameter we are estimating.
confidence level
Assessing the regression model on data other than the sample data that was used to generate the model is known as _____.
cross-validation
In a linear regression model, the variable that is being predicted or explained is known as ______. It is denoted by y and is often referred to as the response variable.
dependent variable
A variable used to model the effect of categorical independent variables in a regression model is known as a ______.
dummy variable
In the simple linear regression model, the _____ accounts for the variability in the dependent variable that cannot be explained by the linear relationship between the variables.
error term
The ____ is the range of values of the independent variables used in the data to estimate the regression model.
experimental region
Prediction of the mean value of dependent variable y for values of the independent variables x1,x2,,,,,,,,,xq that are outside the experimental range is called _____.
extrapolation
Prediction of the value of the dependent variable outside the experimental region is called _____.
extrapolation
Regression analysis involving one dependent variable and more than one independent variable is known as _____.
multiple regression
A simple random simple of size n from a finite population of size N is a sample selected such that each possible sample of size
n has the same probability of being selected
Fitting a model too closely to sample data, resulting in a model that does not accurately reflect the population is termed as ______.
overfitting
Two approaches to drawing a conclusion in a hypothesis test are ____.
p-value and critical value
A simple random sample of 31 observations was taken from a large population. The sample mean equals 5. 5 is a _____ ?
point estimate
The population parameter value and the point of estimate differ because a sample is not a census of the entire population, but it is being used to develop the _____.
point estimte
The purpose of a statistical inference is to make estimates or draw conclusions about a
population based upon information obtained from the sample
A random sample selected from an infinite population is a sample selected such that each element selected comes from the same ______ and each element is selected ____.
population, independently
A _____ is an interval estimate of an individual y value, given values of the independent variables.
prediction interval
_____ is a statistical procedure used to develop an equation showing how two variables are related.
regression analysis
What are the two decisions that you can make from performing a hypothesis test?
reject the null hypothesis, fail to reject the null hypothesis
The difference between the observed value of the dependent variable and the value predicted using the estimated regression equation is known as the _____.
residual
Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed: Ho: u = 11, Ha: u > 11
right-tailed
The value of the _____ is used to esteem the value of the population parameter.
sample statistic
a _____ is used to visualize sample data graphically and to draw preliminary conclusions about the possible relationships between the variables.
scatter chart
a regression analysis involving one independent variable and one dependent variable is referred to as a ______.
simple linear regression
In simple linear regression analysis the quantity that gibes the amount by which the dependent variable changes for a unit change in the independent variable is called the ____.
slope of the regression line
In simple linear regression model, y= B0 + B1x + k the parameter of B1 represents the _____.
slope of the true regression line
A normally distributed error term with a mean of zero would ______.
allow more accurate modeling
Which statement is not true?
Failing to reject the null hypothesis when it is false is a Type 1 error.
For a population with an unknown distribution, the form of the sampling distribution of the sample mean is ______.
approximately normal for large sample sizes
In a random sample of 400 registered voters, 120 indicated they plan to vote for Trump for President. Determine a 95% confidence interval for the proportion of all registered voters who will vote for Trump.
(0.25,0.34)
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion?
0.039
A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ= 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean about of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce the parts will be determined. If the switch is made to the new procedure,the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypothesis Ho:μ ≥ 45 hours and Ha:μ < 45 hours. Determine the p value of the test statistic if the sample mean amount of time is x̄ = 43.118 hours with the sample standard deviation is x=5.5 hours.
0.04999
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the point estimate of the proportion of the population that logged onto Facebook that day?
0.35
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. Compute the 95% confidence interval for the population proportion.
0.35 ± 1.96 √
What would be the coefficient of determination if the total sum of squares (SST) is 23.29 and the sum of squares due to regression (SSR) is 10.03?
0.43
What would be the value of the sum of squares due to regression (SSR) if the total sum of squares (SST) is 25.32 and the sum of squares due to error (SSE) is 6.89?
18.43
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the number of pushups can be done is approximately normal. If we would like to capture the population mean with 95% confidence the margin of error would be
2.262(9/√10)
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. Which of the following statements is true?
2.876
In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is _____.
23
The t value for a 99% confidence interval estimation based upon a sample of size 10 is ____.
3.249
A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the number of pushups can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is _____?
8.56 to 21.40
________ is used to test the hypothesis that the values of the regression parameters B1,B2,,,,B4 are all zero.
An F test
the population parameters that describe the Y intercept and slope of a line relating y and x, respectively, are ___.
B 0 and B 1
A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time μ= 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean about of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce the parts will be determined. If the switch is made to the new procedure,the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypothesis Ho:μ ≥ 45 hours and Ha:μ < 45 hours. If the sample mean amount of time is x̄ = 43.118 hours with the sample standard deviation is x = 5.5 hours, give the appropriate conclusion for a=0.025
Do not reject Ho, do not switch to the new procedure.
The owners of a fast food restaurant have automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, some variation in this amount. The company does not want the machine to systemically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?
Ho:u = 12, Ha:u ≠ 12.
A pizza shop advertises that they deliver in 30 minutes or less or its free. People who Iive in homes that are located on the opposite side of town believe that it will take the pizza shop longer than 30 minutes to make and deliver the pizza. Write the null and alternative hypothesis that can be used to conduct a significance test.
Ho:u ≤ 30, Ha:u >30.
The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are _____.
Ho:u ≥ 50.1, Ha: u <50.1
______ refers to the scenario at which the relationship between the dependent variable and one independent variable is different at different values of a second independent variable.
Interaction
_____ refers to the use of sample data to calculate a range of values that is believed to include the value of the population parameter.
Interval estimation
__________ refers to the degree of correlation among independent variables in a regression model.
Multicollinearity
Which of the following regression models is used to model a nonlinear relationship between the independent and dependent variables by including the independent variable and the square of the independent variable in the model?
Quadratic regression model
Which statement is not true?
Rejecting the null hypothesis when it is a Type II error.
The scatter chart below displays the residuals verses the dependent variable, t. Which of the following conclusions can be drawn based upon this scatter chart? (CHART: POINTS SCATTERED IN "vvv" SHAPE)
Residuals are not independent
The basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population means is ______.
The central limit theorem
The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? (CHART: POINTS SCATTERED IN "V" SHAPE)
The model fails to capture the relationship between the variables accurately.
The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn based upon this scatter chart? (CHART: POINTS SCATTERED RANDOMLY)
The residual distribution is not normally distributed.
The scatter chart below displays the residuals verses the dependent variable, x. Which of the following conclusions can be drawn from the scatter chart given below? (CHART: POINTS SCATTERED IN "<" SHAPE)
The residuals have an increasing variance as the dependent variable increases.
If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to ______.
be an unbiased estimator of the population parameter
______ is the data set used to build the candidate models.
Training set
larger values of a have the disadvantage of increasing the probability of making a ____.
Type 1 error
_______ refers to the data used to compare the model forecasts and ultimately pick a model for predicting values of the dependent variable.
Validation set
A sample of 37 AA batteries had a mean lifetime of 584 hours. A 95% confidence interval for the population mean was 579.2 < μ < 588.8. Which statement is the correct interpretation of the results?
We are 95% confident that the mean lifetime of all the bulbs in the population is between 579.2 hours and 588.8 hours.
The proportion of dental procedures that are extractions is 0.16. Which of the following exemplifies a Type 1 error in this situation?
We reject the claim that the proportion of dental procedures that are extractions of 0.16 when the proportion is actually 0.16.
A variable used to model the effect of categorical independent variables in a regression model which generally takes only the value zero or one is called ____.
a dummy variable
A type 1 error is committed when ____.
a true null hypothesis is rejected
The finite correction factor should be used in the computation of the standard deviation of the sample mean and the standard population when n / N is
greater than 0.05
The process of making a conjecture about the value of a population parameter, collecting sample data that can be used to access this conjecture, measuring the strength of the evidence against the conjecture that is provided by the sample, and using these results to draw a conclusion about the conjecture is known as ______.
hypothesis testing
A one-tailed test is a hypothesis test in which the rejection region is _____.
in one tail of the sampling distribution
In a linear regression model, the variable used for predicting or explaining the values of the response variable are known as the _____. It is denoted by x.
independent variable
An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the
interval estimate
The coefficient of determination _____.
is used to evaluate the goodness of fit
The prospecified value of the independent variable at which its relationship with the dependent variable changes I in a piecewise linear regression model is referred to as the _____.
knot
A null and alternative hypothesis for one proportion z test are given as Ho:p=8,Ha:p<0.8. This hypothesis test is ______.
lower tailed
Statistical significance at the 0.01 levelis ______ than significance at the 0.05 level.
more difficult to achieve
You are _____ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance
more likely
The degree of correlation among independent variables in a regression model is called ______.
multicollinearity