Stats Test 3
Goodness-of-fit hypothesis tests may be left-tailed, right-tailed, or two-tailed.
Which of the following is NOT true of the goodness-of-fit test? Choose the correct answer below. A. Expected frequencies need not be whole numbers. B. If expected frequencies are not all equal, then we can determine them by Eequalsnp for each individual category, where n is the total number of observations and p is the probability for the category. C. If expected frequencies are equal, then we can determine them by Upper E equals StartFraction n Over k EndFraction , where n is the total number of observations and k is the number of categories. D. Goodness-of-fit hypothesis tests may be left-tailed, right-tailed, or two-tailed.
One requirement of this method is that np >5 and nq >5.
Which of the following is NOT true of using the binomial probability distribution to test claims about a proportion?
In any design, if the conclusion is that the differences among the means are significant, the differences are explained by the factor used.
Which of the following is NOT true of one-way analysis of variance experimental design? Choose the correct answer below. A. In any design, if the conclusion is that the differences among the means are significant, the differences are explained by the factor used. Your answer is correct.B. Using a rigorously controlled design is one way to reduce the effect of extraneous factors. C. Good results require that experiments be carefully designed and executed. D. A completely randomized experimental design is one way to reduce the effect of extraneous factors.
a mathematical model
_______ is a mathematical function that describes real-world data.
residual
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.
regression equation
Given a collection of paired sample data, the ____________________ ^y =b0+b1x algebraically describes the relationship between the two variables, x and y.
explained
The _______ deviation is the vertical distance ^y-y bar, which is the distance between the predicted y-value and the horizontal line passing through the sample mean y bar.
total
The _______ deviation of (x,y) is the vertical distance y-y bar, which is the distance between the point (x,y) and the horizontal line passing through the sample mean y bar.
standard error of estimate
The _______ is a measure of the differences between the observed sample y-values and the predicted values ^y with caret that are obtained using the regression equation.
null
The _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value
test statistic
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
linear correlation coefficient r
The ______________ measures the strength of the linear correlation between the paired quantitative x- and y-values in a sample.
adjusted coefficient of determination
The _______________ is the multiple coefficient of determination Upper R squared modified to account for the number of variables and the sample size.
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 property of the linear correlation coefficient r? Choose the correct answer below. A. The value of r is not affected by the choice of x or y. B. The value of r measures the strength of a linear relationship. C. The value of r is always between minus1 and 1 inclusive. D. The linear correlation coefficient r is robust. That is, a single outlier will not affect the value of r.
The mean of the chi-square distribution is 0.
Which of the following is NOT a property of the chi-square distribution? A. The chi-square distribution is different for each number of degrees of freedom, df equals n minus 1. B. The mean of the chi-square distribution is 0. Your answer is correct. C. The values of chi-square can be zero or positive, but they cannot be negative. D. The chi-square distribution is not symmetric.
The form of the confidence interval utilizes the same variance as when testing claims using hypothesis tests.
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? Choose the correct answer below. A. The variance of the differences between two independent random variables is the sum of their individual variances. B. The form of the confidence interval utilizes the same variance as when testing claims using hypothesis tests. Your answer is correct. C. The pooled estimate of the common value of p 1 and p 2 ```````````x1+x2 is p overbar= --------- ```````````n1+n2 D. Since ^p1 and ^p2 are each approximated by a normal distribution, the difference ^p1 - ^p2 will also be approximated by a normal distribution with mean p 1-p 2
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 requirement for testing a claim about a mean with sigma known?
The sample mean, x overbar is greater than 30.
Which of the following is NOT a requirement for testing a claim about a population mean with sigma known?
The population must be skewed to the right.
Which of the following is NOT a requirement for testing a claim about a standard deviation or variance? A. The sample is a simple random sample. B. The chi-square distribution is used. C. The population must be skewed to the right. Your answer is correct. D. The population has a normal distribution.
One of the populations is normally distributed.
Which of the following is NOT a requirement for testing a claim about two population standard deviations or variances? Choose the correct answer below. A. The populations are independent. B. This test requires that both populations have normal distributions. C. One of the populations is normally distributed. Your answer is correct.D. The two samples are simple random samples.
The samples are matched or paired in some way.
Which of the following is NOT a requirement for using one-way analysis of variance for testing equality of three or more population means? Choose the correct answer below. A. The samples are matched or paired in some way. Your answer is correct.B. The populations have distributions that are approximately normal. C. The samples are simple random samples of quantitative data. D. The different samples are from populations that are categorized in only one way.
If rgreater than1, then there is a positive linear correlation.
Which of the following is NOT a requirement in determining whether there is a linear correlation between two variables? Choose the correct answer below. A. Any outliers must be removed if they are known to be errors. B. If rgreater than1, then there is a positive linear correlation. Your answer is correct.C. A scatterplot should visually show a straight-line pattern. D. The sample of paired data is a simple random sample of quantitative data.
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 requirement of testing a claim about a population proportion using a formal method of hypothesis testing?
The degrees of freedom are n-2
Which of the following is NOT a requirement of testing a claim about the mean of the differences from dependent samples? Choose the correct answer below. A. The degrees of freedom are nminus2. Your answer is correct.B. Either the number of pairs of sample data is larger than 30 or the pairs have differences that are from a population having a distribution that is approximately normal, or both. C. The samples are simple random samples. D. The sample data are dependent.
The two samples are dependent.
Which of the following is NOT a requirement of testing a claim about two population means when sigma 1 and sigma 2 are unknown and not assumed to be equal? Choose the correct answer below. A. Either the two sample sizes are large (n 1 greater than30 and n 2 greater than 30) or both samples come from populations having normal distributions, or both of these conditions are satisfied. B. The two samples are independent. C. The two samples are dependent. Your answer is correct. D. Both samples are simple random samples.
The sample is at least 5% of the population.
Which of the following is NOT a requirement of testing a claim or constructing a confidence interval estimate for two population portions? Choose the correct answer below. A. The sample proportions are from two simple random samples that are independent. B. The sample is at least 5% of the population. Your answer is correct. C. For each of the two samples, the number of failures is at least 5. D. For each of the two samples, the number of successes is at least 5.
For each category, the observed frequency is at least 5.
Which of the following is NOT a requirement to conduct a goodness-of-fit test? Choose the correct answer below. A. For each category, the expected frequency is at least 5. B. For each category, the observed frequency is at least 5. Your answer is correct.C. The sample data consist of frequency counts for each of the different categories. D. The data have been randomly selected.
dummy variable
A dichotomous variable with the two possible values of 0 and 1 is called a _____________.
least-squares property
A straight line satisfies the __________________ if the sum of the squares of the residuals is the smallest sum possible.
dichotomous variable
A variable with only two possible discrete values is a _________
multiple regression
A(n) ___________ equation expresses a linear relationship between a response variable y and two or more predictor variables.
A type I error is making the mistake of rejecting the null hypothesis when it is actually false
Which of the following is NOT a true statement about error in hypothesis testing?
Use the regression line for predictions that 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? Choose the correct answer below. A. Find and compare values of Upper R squared. B. Use common sense and think about what you are modeling. C. Look for a pattern in the graph. D. Use the regression line for predictions that go far beyond the scope of the available sample data.
We often know that sigma 1 equals sigma 2
Which of the following is NOT an advantage of pooling sample variances? Choose the correct answer below. A. Hypothesis tests have more power. B. Confidence intervals are a little narrower. C. The number of degrees of freedom is a little higher. D. We often know that sigma 1 equals sigma 2.
Correlation does not imply causality
Which of the following is NOT one of the three common errors involving correlation? Choose the correct answer below. A. Mistaking no linear correlation with no correlation B. Correlation does not imply causality Your answer is correct.C. The use of data based on averages D. The conclusion that correlation implies causality
The inequality symbol in the alternative hypothesis points away from the critical region.
Which of the following is NOT true about the tails in a distribution?
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 about P-values in hypothesis testing?
If |r|greater thancritical 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.
Which of the following is NOT true for a hypothesis test for correlation? Choose the correct answer below. A. If |r|less than or equalscritical 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. B. If the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation. C. If the P-value is less than or equal to the significance level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation. D. If |r|greater thancritical 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.
A confidence interval is used to test a claim about two population proportions.
Which of the following is NOT true of confidence interval estimates of the difference between two population proportions? Choose the correct answer below. A. The confidence interval uses a standard deviation based on estimated values of the population proportions. B. A confidence interval is used to test a claim about two population proportions. Your answer is correct. C. A confidence interval is used to estimate the difference between two population proportions. D. If a confidence interval estimate of p 1 minus p 2 does not include 0, we have evidence suggesting that p 1 and p 2 have different values.
If the F test statistic is large, then the P-value will be large.
Which of the following is NOT true of the F test statistic? Choose the correct answer below. A. F= ms(treatment)/Ms(error) when testing with unequal sample sizes B. If the F test statistic is large, then the P-value will be large. Your answer is correct.C. The F test statistic is never negative. D. F=(variance between samples)/ (Variance with samples)
Small values of F are evidence against sigma 2/1 =sigma 2/2
Which of the following is NOT true of the F test? Choose the correct answer below. A. The count five method is a relatively simple alternative to the F test, and it does not require normally distributed populations. B. Small values of F are evidence against sigma Subscript 1 Superscript 2 Baseline equals sigma Subscript 2 Superscript 2. Your answer is correct.C. All one-tailed F tests will be right-tailed.
This test is very resistant to departures from normal distributions.
Which of the following is NOT true of the F test? Choose the correct answer below. A. This test uses the F distribution. B. This test is very resistant to departures from normal distributions. Your answer is correct.C. This test requires that both populations have normal distributions. D. This test compares two population variances or standard deviations.
A small chi squared test statistic leads us to conclude that there is not a good fit with the assumed distribution.
Which of the following is NOT true of the chi squared test statistic? Choose the correct answer below. A. If the observed and expected frequencies are not close, the chi squared test statistic will be large and the P-value will be small. B. The chi squared test statistic is based on differences between the observed and expected values. C. A small chi squared test statistic leads us to conclude that there is not a good fit with the assumed distribution.
treatment
A _______ is a characteristic used in ANOVA that allows us to distinguish different populations from one another.
prediction interval
A _______ is an interval estimate of a predicted value of y.
correlation
A __________ exists between two variables when the values of one variable are somehow associated with the values of the other variable.
hypothesis test
A _____________ is a procedure for testing a claim about a property of a population.
goodness-of-fit test
A _____________ is used to test the hypothesis that an observed frequency distribution fits (or conforms to) some claimed distribution.
residual plot
A ______________ is a scatterplot of the (x,y) values after each of the y-coordinate values has been replaced by the residual value yminusModifyingAbove y with caret.
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.
If the F test statistic is large, then the P-value will be large.
outlier
In a scatterplot, a(n) ______________ is a point lying far away from the other data points.
marginal change
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.
influential points
Paired sample data may include one or more ___________, which are points that strongly affect the graph of the regression line.
Power
The _________ of a hypothesis test is the probability (1 minus beta) of rejecting a false null hypothesis.
y
The coefficient of determination, r squared, is the amount of variation in _______ that is explained by the regression line.
one-way analysis of variance
The method of _______ is used for tests of hypotheses that three or more population means are equal.
independent
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.
dependent
Two samples are ________________ if the sample values are paired.
Using dependent samples with paired data is generally better than using two independent samples.
What design principle is stressed for experiments or observational studies? Choose the correct answer below. A. The methods for dependent samples can be used for any matched pairs. B. Using dependent samples with paired data is generally better than using two independent samples. Your answer is correct.C. Using two independent samples is the best choice for accurate results. D. When using paired data, keep the sample very small in order to keep the data manageable.
scatterplot
When determining whether there is a correlation between two variables, one should use a ____________ to explore the data visually.
Use the regression line for predictions only if the data go far beyond the scope of the available sample data.
When making predictions based on regression lines, which of the following is not listed as a consideration? Choose the correct answer below. A. Use the regression equation for predictions only if the graph of the regression line on the scatterplot confirms that the regression line fits the points reasonably well. B. Use the regression line for predictions only if the data go far beyond the scope of the available sample data. Your answer is correct.C. If the regression equation does not appear to be useful for making predictions, the best predicted value of a variable is its point estimate. D. Use the regression equation for predictions only if the linear correlation coefficient r indicates that there is a linear correlation between the two variables.
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 criterion for making a decision in a hypothesis test?
multi-linear
Which of the following is NOT a generic mathematical model? Choose the correct answer below. A. Power B. Multi-linear C. Exponential D. Linear
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 a guideline for finding the best multiple regression equation? Choose the correct answer below. A. Consider the P-value to select an equation having overall significance. B. Consider equations with high values of adjusted Upper R squared, and try to include only a few variables. C. Use common sense and practical considerations to include or exclude variables. D. If two predictor values have a very high linear correlation coefficient, both should be included in finding the multiple regression equation.
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 principle of making inferences from dependent samples? Choose the correct answer below. A. The hypothesis test and confidence interval are equivalent in the sense that they result in the same conclusion. B. The t-distribution serves as a reasonably good approximation for inferences from dependent samples. C. Testing the null hypothesis that the mean difference equals 0 is not equivalent to determining whether the confidence interval includes 0. Your answer is correct.D. There is some relationship whereby each value in one sample is paired with a corresponding value in the other sample.
The F distribution is bell-shaped.
Which of the following is NOT a property of the F distribution? Choose the correct answer below. A. The F distribution is bell-shaped. Your answer is correct.B. The exact shape of the F distribution depends on the two different degrees of freedom. C. Values of the F distribution cannot be negative. D. The F distribution is not symmetric.
The F distribution is bell shaped.
Which of the following is NOT a property of the F distribution? Choose the correct answer below. A. Values in the F distribution cannot be negative. B. The F distribution is bell shaped. Your answer is correct.C. The exact shape of the F distribution depends on the two different degrees of freedom. D. The F distribution is not symmetric.
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 dealing with independent samples? Choose the correct answer below. A. 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. Your answer is correct. B. The null hypothesis µ 1 equalsµ 2 or µ 1 minus µ 2 equals 0 can be tested using the P-value method, the traditional method, or by determining if the confidence interval limits for µ 1 minusµ 2 contain 0. C. The confidence interval estimate of µ 1 minusµ 2 is left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus Upper E less than left parenthesis µ 1 minus µ 2 right parenthesis less than left parenthesis x overbar 1 minus x overbar 2 right parenthesis plus Upper E . D. When making an inference about the two means, the P-value and traditional methods of hypothesis testing result in the same conclusion as the confidence interval method.
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 investigating two population proportions? Choose the correct answer below. A. Testing for equality of two population proportions cannot be done by determining whether there is an overlap between two individual confidence interval estimates of the two individual population proportions. B. When testing a claim about two population proportions, the P-value method and the classical method are equivalent. C. The P-value method or the classical method of hypothesis testing can be used to test a claim about two population proportions. D. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.
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 testing a claim about a standard deviation or variance? A. The table for finding P-values does not usually give exact P-values as it only includes select values of alpha and selected numbers of degrees of freedom. B. The chi squared test is not robust against a departure from normality. C. The P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results. Your answer is correct. D. The condition of a normally distributed population is a much stricter requirement for the chi squared test than for the t test or the z test.
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?
Small F test statistics indicate that the decision is to reject the null hypothesis of equal means.
Which of the following is NOT true when using one-way analysis of variance for testing equality of three or more population means? Choose the correct answer below. A. The numerator of the F test statistic measures variation between sample means. B. The conclusion that there is sufficient evidence to reject the claim of equal population means does not indicate a particular mean is different from the others. C. Small P-values indicate that the decision is to reject the null hypothesis of equal means. D. Small F test statistics indicate that the decision is to reject the null hypothesis of equal means.
The Student t distribution has a mean of t=0 and a standard deviation of s=1.
Which of the following is not a characteristic of the t test?
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 regression analysis? Choose the correct answer below. A. The method for regression analysis line is not robust. It is seriously affected by a small departure from a normal distribution. B. Outliers can have a strong effect on the regression equation, so remove any outliers if they are known to be errors. C. The sample of paired (x,y) data is a random sample of quantitative data. D. Visual examination of the scatterplot shows that the points approximate a straight-line pattern.
The population mean, mu, is equal to 1.
Which of the following is not a requirement for testing a claim about a population with sigma not known?
Use the table in the book to find the P-value rounded to at least 4 decimal places
Which of the following is not a strategy for finding P-values with the Student t distribution?
dependent variable
Which of the following is not equivalent to the other three? Choose the correct answer below. Predictor variable Dependent variable Explanatory variable Independent variable
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 when sigma is unknown
We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase.
Which of the following statements about correlation is true? Choose the correct answer below. A. We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values decrease. B. We say that there is a positive correlation between x and y if the x-values increase as the corresponding y-values increase. Your answer is correct.C. We say that there is a positive correlation between x and y if there is no distinct pattern in the scatterplot. D. We say that there is a negative correlation between x and y if the x-values increase as the corresponding y-values increase.
