Math exam 3
Which of the following statements are true concerning the mean of the differences between two dependent samples (matched pairs)?
-If one wants to use a confidence interval to test the claim that mu (u looking symbol) with little d symbol > 0 with a 0.05 significance level, the confidence interval should have a confidence level of 90%. -If one has fifteen matched pairs of sample data, there is a loose requirement that the fifteen differences appear to be from a normally distributed population.
Which of the following is NOT true about P-values in hypothesis testing?
. The P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.
Which of the following is NOT true when investigating two population proportions?
A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
Which of the following is NOT true when testing a claim about a proportion?
A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
Which of the following is NOT true of confidence interval estimates of the difference between two population proportions?
A confidence interval is used to test a claim about two population proportions
Which of the following is NOT true of the X^2 test statistic?
A small X^2 test statistic leads us to conclude that there is not a good fit with the assumed distribution.
Which of the following is NOT a true statement about error in hypothesis testing?
A type I error is making the mistake of rejecting the null hypothesis when it is actually false.
A: If s 2/1 represents the larger of two sample variances, can the F test statistic ever be less than 1? B: Can the F test statistic ever be a negative number? C: If testing the claim that sigma( o looking symbol) 2/1 not equals sigma ( o looking symbol) 2/2, what do we know about the two samples if the test statistic is F = 1? D: Is the F distribution symmetric, skewed left, or skewed right?
A: No, because the ratio s 2/1 / s 2/2 will always be greater than 1. B: No, because sample variances cannot be negative, and the result of dividing the squares of two non negative numbers is never negative C: The two samples have the same standard deviation (or variance). D: The F distribution is skewed right.
Which of the following is NOT a requirement to conduct a goodness-of-fit test?
For each category, the observed frequency is at least 5.
Which of the following is NOT true of the goodness-of-fit test?
Goodness-of-fit hypothesis tests may be left-tailed, right-tailed, or two-tailed.
A _____________ is a procedure for testing a claim about a property of a population.
Hypothesis Test
Which of the following is NOT true of the F test statistic?
If the F test statistic is large, then the P-value will be large.
Which of the following is NOT true?
If the decision from ANOVA is to reject the equality of the three population means, the particular mean that differs from the others is known.
Which of the following is NOT a requirement for testing a claim about a mean with sigma (o looking symbol) known?
If the sample results (or more extreme results) cannot easily occur when the null hypothesis is true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is true, so we do not reject the assumption.
Which of the following is NOT a criterion for making a decision in a hypothesis test?
If the P-value is less than 0.05, the decision is to reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Which of the following is NOT a guideline for finding the best multiple regression equation?
If two predictor values have a very high linear correlation coefficient, both should be included in finding the multiple regression equation.
Which of the following is NOT true of one-way analysis of variance experimental design?
In any design, if the conclusion is that the differences among the means are significant, the differences are explained by the factor used.
If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature?
No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.
Which of the following is NOT a requirement for testing a claim about two population standard deviations or variances?
One of the populations is normally distributed.
Which of the following is NOT true of using the binomial probability distribution to test claims about a proportion?
One requirement of this method is that np greater than 5 and nq greater than 5 (One requirement of this method is that np > 5 and nq > 5)
When using the numbers of points scored in each Super Bowl from 1980 to the last Super Bowl at the time that this exercise was written, we obtain the following values of R squared for the different models: linear: 0.002; quadratic: 0.082; logarithmic: 0.003; exponential: 0.005; power: 0.001. Based on these results, which model is best? Is the best model a good model?
Quadratic is best, but it is not a good model.
A ______________ is a scatterplot of the (x,y) values after each of the y-coordinate values has been replaced by the residual value y - y
Residual plot
Which of the following is NOT true when using one-way analysis of variance for testing equality of three or more population means?
Small F test statistics indicate that the decision is to reject the null hypothesis of equal means.
Which of the following is NOT true of the F test?
Small values of F are evidence against sigma (o looking symbol) 2/1 = sigma (o looking symbol) 2/2.
Which of the following is NOT a principle of making inferences from dependent samples?
Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0.
Which of the following is NOT a property of the F distribution?
The F distribution is bell shaped.
Which of the following is NOT a property of the F distribution?
The F distribution is bell-shaped.
Which of the following is not a characteristic of the t test?
The Student t distribution has a mean of t = 0 and a standard deviation of s = 1.
Which of the following is NOT a requirement of testing a claim about the mean of the differences from dependent samples?
The degrees of freedom are n - 2.
What is the difference between the following two regression equations? ^ y = b0 + b1x y = B0 + B1x
The first equation is for sample data; the second equation is for a population.
Which of the following is NOT a reason why the procedures to estimate differences of two proportions or testing a claim about two proportions work?
The form of the confidence interval utilizes the same variance as when testing claims using hypothesis tests.
Which of the following is NOT true about the tails in a distribution?
The inequality symbol in the alternative hypothesis points away from the critical region.
Which of the following is NOT a property of the linear correlation coefficient r?
The linear correlation coefficient r is robust. That is, a single outlier will not affect the value of r.
Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis testing?
The lowercase symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.
Which of the following is NOT a property of the chi-square distribution?
The mean of the chi-square distribution is 0.
Which of the following is not a requirement for regression analysis?
The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution.
Which of the following is NOT a requirement for testing a claim about a standard deviation or variance?
The population must be skewed to the right.
Which of the following is not a requirement for testing a claim about a population with sigma not known?
The population mean, mu (u looking symbol) , is equal to 1.
In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain.
The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the number of successes is at least 5 and the number of failures is at least 5.
Weight = -274 + 0.426 Length + 12.1 Chest Size Identify the response and predictor variables in this regression equation.
The response variable is weight and the predictor variables are length and chest size.
Which of the following is NOT a requirement of testing a claim or constructing a confidence interval estimate for two population portions?
The sample is at least 5% of the population.
Determine whether the samples are independent or dependent. To test the effectiveness of a drug comma cholesterol levels are measured in 150 men before and after the treatment.
The samples are dependent because there is a natural pairing between the two samples.
Determine whether the samples are independent or dependent. Upper A data set includes the age at marriage for 60 randomly selected married couples.
The samples are dependent because there is a natural pairing between the two samples.
Determine whether the samples are independent or dependent. Upper A data set includes the morning and evening temperature for the last 250 days.
The samples are dependent because there is a natural pairing between the two samples.
Determine whether the samples are independent or dependent. Upper A data set included the daily number of words spoken by 60 randomly selected women and 60 randomly selected men.
The samples are independent because there is not a natural pairing between the two samples.
Which of the following is NOT a requirement for testing a claim about a population mean with sigma (o looking symbol) known?
The sample mean, x is greater than 30.
Which of the following is NOT a requirement of testing a claim about two population means when sigma1 (o looking symbol) and sigma2 (o looking symbol) are unknown and not assumed to be equal?
The two samples are dependent.
Which of the following is NOT true when dealing with independent samples?
The variance of the differences between two independent random variables equals the variance of the first random variable minus the variance of the second random variable.
Which of the following is NOT true when testing a claim about a standard deviation or variance?
The P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.
Which of the following is not true when using the confidence interval method for testing a claim about mu (u looking symbol) when sigma (o looking symbol) is unknown?
The P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.
Which of the following is NOT true of the F test?
This test is very resistant to departures from normal distributions.
Identify the type 1 error and the type 2 error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.15.
Type 1 error: Reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually 0.15. Type 2 error: Fail to reject the claim that the proportion of people who write with their left hand is 0.15 when the proportion is actually different from 0.15.
Identify the type 1 error and the type 2 error that correspond to the given hypothesis. The percentage of adults who have a job is greater than 88 %.
Type 1 error: Reject the null hypothesis that the percentage of adults who have a job is equal to 88 % when that percentage is actually equal to 88 %. Type 2 error: Fail to reject the null hypothesis that the percentage of adults who have a job is equal to 88 % when that percentage is actually greater than 88 %.
Identify the type 1 error and the type 2 error that correspond to the given hypothesis. The percentage of high school students who graduate is less than 55 %.
Type 1 error: Reject the null hypothesis that the percentage of high school students who graduate is equal to 55 % when that percentage is actually equal to 55 %. Type 2 error: Fail to reject the null hypothesis that the percentage of high school students who graduate is equal to 55 % when that percentage is actually less than 55 %.
Identify the type 1 error and the type 2 error that correspond to the given hypothesis. The percentage of adults who retire at age 65 is equal to 62 %.
Type 1 error: Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually equal to 62 % Type 2 error: Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually different from 62 %.
When making predictions based on regression lines, which of the following is not listed as a consideration?
Use the regression line for predictions only if the data go far beyond the scope of the available sample data.
Which of the following is NOT among the three basic rules for developing a good mathematical model?
Use the regression line for predictions that go far beyond the scope of the available sample data.
Which of the following is not a strategy for finding P-values with the Student t distribution?
Use the table in the book to find the P-value rounded to at least 4 decimal places.
What design principle is stressed for experiments or observational studies?
Using dependent samples with paired data is generally better than using two independent samples.
Which of the following is NOT an advantage of pooling sample variances?
We often know that sigma1 (o looking symbol) = sigma2 (o looking symbol) .
Which of the following statements about correlation is true?
We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase.
The _______________ is the multiple coefficient of determination R squared modified to account for the number of variables and the sample size.
adjusted coefficient of determination
A __________ exists between two variables when the values of one variable are somehow associated with the values of the other variable.
correlation
Which of the following is NOT one of the three common errors involving correlation?
correlation does not imply causality
Two samples are ________________ if the sample values are paired.
dependent
Which of the following is not equivalent to the other three?
dependent variable
A variable with only two possible discrete values is a _______________.
dichotomous variable
A dichotomous variable with the two possible values of 0 and 1 is called a _____________.
dummy variable
The _______ deviation is the vertical distance y - y, which is the distance between the predicted y-value and the horizontal line passing through the sample mean y
explained
A _____________ is used to test the hypothesis that an observed frequency distribution fits (or conforms to) some claimed distribution.
goodness of fit test
Which of the following is NOT a requirement in determining whether there is a linear correlation between two variables?
if r > 1 , then there is a positive linear correlation
Which of the following is NOT true for a hypothesis test for correlation?
if | r | > critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.
Two samples are ____________ if the sample values from one population are not related to or somehow naturally paired or matched with the sample values from the other population.
independent
Paired sample data may include one or more ___________, which are points that strongly affect the graph of the regression line.
influential points
A straight line satisfies the __________________ if the sum of the squares of the residuals is the smallest sum possible.
least squares property
The ______________ measures the strength of the linear correlation between the paired quantitative x- and y-values in a sample.
linear correlation coefficient r
In working with two variables related by a regression equation, the _________________ in a variable is the amount that it changes when the other variable changes by exactly one unit.
marginal change
_____________ is a mathematical function that describes real-world data.
mathematical model
Which of the following is NOT a generic mathematical model?
multi-linear
A(n) ___________ equation expresses a linear relationship between a response variable y and two or more predictor variables.
multiple regression
The _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.
null hypothesis
The method of _______ is used for tests of hypotheses that three or more population means are equal.
one way analysis of variance
In a scatterplot, a(n) ______________ is a point lying far away from the other data points.
outlier
The _________ of a hypothesis test is the probability (1minusbeta) of rejecting a false null hypothesis.
power
A _______ is an interval estimate of a predicted value of y.
prediction interval
Given a collection of paired sample data, the ____________________ y = b0 + b1x algebraically describes the relationship between the two variables, x and y.
regression equation
For a pair of sample x- and y-values, the ______________ is the difference between the observed sample value of y and the y-value that is predicted by using the regression equation.
residual
When determining whether there is a correlation between two variables, one should use a ____________ to explore the data visually.
scatterplot
The _______ is a measure of the differences between the observed sample y-values and the predicted values y that are obtained using the regression equation.
standard error of estimate
The ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.
test statistic
Which of the following is NOT a requirement for using one-way analysis of variance for testing equality of three or more population means?
the samples are matched or paired in some way
The _______ deviation of (x,y) is the vertical distance y - y which is the distance between the point (x,y) and the horizontal line passing through the sample mean y
total deviation
A _______ is a characteristic used in ANOVA that allows us to distinguish different populations from one another.
treatment
The coefficient of determination, r squared, is the amount of variation in _______ that is explained by the regression line.
y
