SA Final
As our confidence in an interval estimate increases, the width of the interval
increases
The efficiency of any estimator can be improved by increasing the sample size decreasing the sample size making the sample representative changing the sample
increasing the sample size
In the chi square test of hypothesis, the null hypothesis states that the variables are dependent independent causally related non-random
independent
A survey administered to a sample drawn from a local community finds that a person's political party affiliation is related to whether or not they favor an increase in local sales tax (the headline of a newspaper story based on this poll reads: "Republicans support proposed tax increase"). This is an example of the use of univariate descriptive statistics inferential statistics multivariate descriptive statistics reductionist statistics
inferential statistics
One important function of the least-squares regression equation is that it summarizes all possible scores on the two variables it makes the scattergram symmetrical we can use it to tell if a relationship is linear it allows us to predict Y scores for any value of X
it allows us to predict Y scores for any value of X
For variables measured at the nominal level, measures of association will have a lower limit of _______ and an upper limit of _______
0 ... 1
A social researcher has constructed a measure of racial prejudice and obtained a distribution of scores on this measure from a randomly selected sample of public office holders. The scores were normally distributed with a mean of 45 and a standard deviation of 7. What is the probability that a randomly selected case from the sample will have a score less than 38? 0.4526 0.5018 0.5200 0.1587
0.1587
The probability that a randomly selected case will have a score beyond ± 1.00 standard deviation of the mean is 0.6826 0.5000 0.3174 1/2 of the area of 1 standard deviation
0.3174
The average homicide rate for the cities and towns in a state is 10 per 100,000 population with a standard deviation of 2. If the variable is normally distributed, what is the probability that a randomly selected town will have a homicide rate greater than 8? 0.34 0.68 0.84 0.01
0.84
The mean score on a final chemistry exam was 75, and the standard deviation of the scores was 5. If the distribution is normal and your score was 70, what percentage of the scores was lower than yours? 15.87% 30.00% 34.13% 50.00%
15.87%
The mean age of all graduates of a certain college is 35. If the population distribution is normal, the mean of any sampling distribution of sample mean ages of graduates of this college will be within plus or minus 1 standard deviation of 35 close to 35 35 determined by the size of the distribution
35
The area between the mean and a Z score of +1.50 is 43.32%. This score is higher than _________ of the scores in the distribution. 43.32% 51.50% 57.68% 93.32%
93.32%
When an empirical normal distribution of scores is standardized the mean will become 0 the standard deviation will become 1 each score will be converted to a Z score all of the above
All of the above
A researcher asked a sample of dual career families about the percentage of the family budget contributed by the wife's job (Y) and the total number of children (X). Pearson's r for this relationship is -0.34. Which of the following is an appropriate interpretation of these results? For every dollar contributed by the wife, the number of children increases by .34 For every additional child, the wife must work longer hours Every additional child lowers the economic wellbeing of the family As number of children increase, the percentage of the budget contributed by the wife decreases
As number of children increase, the percentage of the budget contributed by the wife decreases.
Four students have applied to a special program and only one can be accepted. They have taken a battery of 12 tests and all have exactly the same average score. The standard deviation of their test scores are: Student A = 3.12, Student B = 0.27, Student C = 13.45, Student D = 6.45. If consistency of performance is a criteria for acceptance, which of the four students should be selected? A B C D
B
A researcher has found a strong relationship between level of education and income and concludes that "higher levels of education cause higher income." What error has been made? None, the argument is sound Income is only nominal in level of measurement and education is ordinal so they cannot be causally related Since these variables are continuous and interval ratio, they cannot have a causal relationship By itself, association does not prove causation
By itself, association does not prove causation
As measures of association, phi and Cramer's V are especially useful when an ANOVA test has already been conducted percentages have not been calculated cell frequencies are unknown Chi square has already been calculated
Chi square has already been calculated
If you would like to compute a chi-square based measure of association for a 3x4 table, the appropriate measure would be Cramer's V phi lambda the maximum difference
Cramer's V
A researcher has analyzed differences in average College Board scores for random samples of students from four different colleges. The obtained F score is 0.45. What can be concluded about the null hypothesis? Nothing, more information is needed Reject the null hypothesis, the differences did not occur by random chance Fail to reject the null hypothesis, differences are not statistically significant Fail to reject the null hypothesis, differences are statistically significant
Fail to reject the null hypothesis, differences are not statistically significant
In a study of the relationship between geographical mobility (number of times a person has changed residences) and number of friends, Pearson's r² is reported as .40. Which of the following would be a correct interpretation? Mobility explains 16% of the variation in number of friends There is a strong positive relationship between number of friends and mobility As mobility increases, number of friends decreases Mobility explains 40% of the variation in number of friends
Mobility explains 40% of the variation in number of friends
A researcher has numbered all 50 states from 1 to 50 and has calculated a mean of 17.43 for the variable "state of birth." Since the variable is nominal, the mean makes no sense Since the variable is ordinal, we should treat the value of the mean with great caution The variable is interval-ratio and the mean is an appropriate and useful statistic in this case Since this variable is non-empirical, the mean should not be computed
Since the variable is nominal, the mean makes no sense
Ordinal level scales measuring religiosity and personal happiness range from 0 to 100. Which measure of association would be most appropriate to assess the relationship between these two variables? chi square phi gamma Spearman's rho
Spearman's rho
The text reports the results of a test for the significance of the difference in average income for random samples of males and females. Males earned an average of about $17,000 more per year and the Z score computed in step 4 was 6.53. Given these results, which of the following is a reasonable conclusion? The difference is statistically significant, large, and important The difference is not statistically significant and was probably caused by random chance There is no gender gap in income in the United States This difference is statistically significant but quite small.
The difference is statistically significant, large, and important
Very large random samples of Catholics, Protestants, and people with no religious affiliation have been questioned about their opinions on capital punishment. On a ten point scale, the Protestants average 6.8, the Catholics averaged 7.0, and the "Nones" averaged 7.1. These differences were tested by ANOVA and found to be statistically significant. What is the most reasonable conclusion This is a statistically significant and important difference This difference may be statistically significant but it seems unimportant This difference is due to random chance The researcher should have used sample means rather than proportions in this situation
This difference may be statistically significant but it seems unimportant
If people who eat at fast food restaurants become obese, obesity is an independent variable a causal variable a dependent variable none of the above
a dependent variable
A researcher wants to visually display the U.S. divorce rate (an interval-ratio level variable) for the last 50 years. An appropriate format would be a line chart or histogram only a histogram would work in this situation a pie chart none of the above. Data in the form of rate should never be displayed in a chart or graph
a line chart or histogram
If a distribution of test scores has a mean of 70 and a median of 63, the distribution has a few very low scores a mode of 67 a negative skew a positive skew
a positive skew
On all normal curves the area between the mean and +1 standard deviation will be about 34% of the total area about 68% of the total area about 95% of the total area about 99% of the total area
about 34% of the total area
The characteristic(s) of a relationship between two variables that must be analyzed for a full understanding of the relationship is (are) the existence of an association the strength of an association the direction of an association all of the above
all of the above - the existence of an association the strength of an association the direction of an association
The probability that an interval estimate does not include the population value is called the margin alpha an error the odds
alpha
A researcher tested the relationship between occupational prestige and level of approval of a proposal to ban handguns in the state and found a gamma of -0.17. This mean: as prestige goes up, support for the ban goes down the electorate will approve the ban support for the ban is highest among the rich support tends to increase as prestige increases
as prestige goes up, support for the ban goes down
the conditional distributions of Y change, the variables are independent not associated significantly related associated
associated
In the research process, theory is unnecessary is always fully developed before any data is gathered is developed only after the data have been completely analyzed attempts to explain the relationship between phenomenon
attempts to explain the relationship between phenomenon
The research hypothesis (H1) typically states what the researcher expects to find and
contradicts the null hypothesis
If you calculated the standard deviation for a distribution of 20 scores, removed the 5 highest scores and recalculated, the value of the standard deviation would increase stay the same decrease be reduced by five
decrease
A researcher reports a Pearson r of .57 between gender (female = 0, males = 1) and involvement in juvenile delinquency. Which of the following is an appropriate interpretation? females are more delinquent there is no relationship between the variables delinquency increases as gender "increases" only males were delinquent
delinquency increases as gender "increases"
Public opinion polls and election projections are examples of estimation procedures hypothesis testing non-statistical research methods blatant misuse of statistical procedures
estimation procedures
If the regression line showing the effect of education on income has a slope of 1000 the variables are not related every year of education increases income by 1000 every change in education increases income the Y intercept would be 1.00
every year of education increases income by 1000
If the critical region begins at Z (critical) = ± 2.56 and the test statistic is - 2.50, we fail to reject the null hypothesis reject the null hypothesis cannot make a decision because the test statistic is so close to the critical region change the alpha level
fail to reject the null hypothesis
In tests of significance, if the test statistic does NOT fall in the critical region, we conclude that the population distribution is normal reject the null hypothesis fail to reject the research hypothesis conclude that our alpha level was too low
fail to reject the research hypothesis
A bivariate table shows the association between gender and whether or not a person ever attends formal religious services. Lambda was .34. What may be concluded? women are more likely to attend church men are more likely to attend church knowing a person's gender improves our ability to predict whether or not they attend religious services by 34% knowing whether a person attends religious services improves our ability to predict their gender by 34%
knowing a person's gender improves our ability to predict whether or not they attend religious services by 34%
When the null hypothesis in the chi square test for independence is true, there should be large difference between the observed frequencies and the expected frequencies little difference between the observed frequencies and the expected frequencies no difference between the observed frequencies and the marginals no difference between the row and the column marginals
little difference between the observed frequencies and the expected frequencies
To increase the probability that a confidence interval will include the population parameter lower the alpha level raise the alpha level increase the bias of the sample statistic set efficiency to zero
lower the alpha level
If male and female college students work an average of 15 hours per week during the school year and the standard deviation is 5.4 for male students and 2.3 for female students, what may we conclude? males are more heterogeneous on this variable females are more heterogeneous on this variable the median number of hours worked is the same the modal number of hours worked is the same
males are more heterogeneous on this variable
Two sample statistics are unbiased estimators. They are means and proportions means and standard deviations medians and modes proportions and percentages
means and proportions
Tests of significance tell us if our results are non-random. To investigate the strength and direction of relationships, we must use Chi square tests ANOVA percentages measures of association
measures of association
Income distributions almost always have a positive skew (since there are only a few very wealthy people). Therefore, the preferred measure of central tendency for this variable would be the mode median mean none of the above
median
Dummy variables make it possible to include ________ in regression analysis nominal variables variables measuring intelligence interval-ratio variables variables with more than two scores
nominal variables
On a test, the numbers used to identify the questions would be __________ in level of measurement while the number of correct responses would be _____________. nominal, interval-ratio interval-ratio, nominal interval-ratio, ordinal ordinal, nominal
nominal, interval-ratio
The sampling distribution for chi squares is shaped like any other normal curve not normally distributed bimodal all of the above
not normally distributed
A researcher is investigating an outreach program that is intended to reduce the number of homeless children in the state. In this situation, it would be appropriate to use a _______ test of significance random non-probability one-tailed zero alpha
one-tailed
For a single variable measured at the nominal level, an appropriate graph would pie chart histogram frequency polygon bivariate table
pie chart
Rejection of the null hypothesis in the two-sample case implies that the samples are different on the trait of interest populations from which the samples are drawn are different on the trait of interest samples are not different on the trait of interest populations from which the samples are drawn are not different on the trait of interest
populations from which the samples are drawn are different on the trait of interest
Which assumption must be true in order to justify the use of hypothesis testing? random sampling interval-ratio level of measurement very large samples samples have been stratified
random sampling
Which of the following is NOT an assumption required for a test of hypothesis with a single sample mean? a representative sample sample size (N) larger than 1,000 normal sampling distribution interval-ratio level of measurement
sample size (N) larger than 1,000
A researcher reports a chi square (obtained) of 75.34 (alpha =.05, df = 1, chi square (critical) = 3.84, N = 13,678). The researcher claims that the relationship is extremely significant. What issue should be raised? degrees of freedom are much too small for a sample this large. alpha is too low sample size is very large and the actual relationship between the variables might be trivial the value for c2 (critical) is much too low
sample size is very large and the actual relationship between the variables might be trivial
In testing for the significance of the difference between two sample means when the sample size is small, we may assume equal population variances if sample sizes are exactly the same sample sizes are varied sample sizes are approximately equal none of the above, we cannot assume equal population variance
sample sizes are approximately equal
From a university population, random samples of 45 seniors and 37 freshmen have been given a scale that measures sexual experiences. The freshmen report an average of 1.6 sexual partners over their lifetimes while seniors report an average of 2.5 partners. The t (obtained) for this difference was -3.56 while the t(critical) was ± 2.34. What can be concluded? there is no significant difference between the classes seniors and freshman are significantly different in their sexual experiences freshman are more sexually active sexual mores are deteriorating
seniors and freshman are significantly different in their sexual experiences
When we decide on a value for alpha, we are defining the likelihood of accepting the alternative hypothesis establishing whether the test will be one or two tailed setting the probability of committing a Type I error setting the probability of a one-tailed test
setting the probability of committing a Type I error
Scattergrams do NOT give information about the _____________ of a relationship strength direction linearity significance
significance
Random samples of men and women have been given a scale that measures their support for gun control. Men average 10.2 with standard deviation of 5.3. Women also average 10.2 but their standard deviation is 1.8. How could these results be dealt with appropriately? test the difference in the sample means for statistical significance since the sample means are the same value, there is no need to conduct any tests; these results cannot be significant a one-tailed test of significance is called for a test of significance with a very high alpha level (a > 0.10) is called for
since the sample means are the same value, there is no need to conduct any tests; these results cannot be significant
As the standard deviation of a normal distribution increases, the percentage of the area between ± 1 standard deviation will increase stay the same decrease become non-symmetrical
stay the same
The purpose of univariate descriptive statistics is to summarize relationships between many variables display the essential meaning of variables measured at the interval-ratio level combine nominal and ordinal variables summarize a single variable
summarize a single variable
When we have an interval-ratio dependent variable and are comparing two groups, the appropriate test of significance is the ________ . When we have an interval-ratio dependent variable and are comparing three or more groups, the appropriate test of significance is the ________ .
t test ... ANOVA
From a university population, random samples of 145 men and 237 women have been asked if they have ever cheated in a college class. 8% of the men and 6% of the women said that they have. What is the appropriate test to assess the significance of this difference? test for the significance of the difference between two sample proportions, large samples test for the significance of the difference between two sample proportions, small samples test for the significance of the difference between two sample proportions, matched samples test for the significance of the difference between two sample means, large samples
test for the significance of the difference between two sample proportions, large samples
In a ranked list of 25 scores, the median is the score of the 12th case the 13th case the average of the scores of the 12th and 13th cases the average of all of the scores
the 13th case
A researcher conducted a survey to determine if older people have different feelings about abortion than younger people. He used an alpha level of 0.05 (Zcritical = ±1.96) to test for significance and found that his computed test statistic was 2.76. He may conclude that the difference occurred by random chance the difference did not occur by random chance the samples are not independent the alpha level was too low
the difference did not occur by random chance
Samples of Republicans and Democrats have been tested for their level of support for welfare reform and the null hypothesis has been rejected. What may we conclude? the difference is significant, there are differences between the parties on this issue the difference is significant, the parties are the same on this issue the difference is not significant a Type I error has occurred
the difference is significant, there are differences between the parties on this issue
In a campaign debate over the level of prosperity in the state, the incumbent governor says: "average income is $53,000." His opponent responds "the average citizen earns only $38,000." Both statements are true. This is possible because the governor is citing the median the opponent is using the mode the opponent is using the mean the governor is using the mean
the governor is using the mean
The greater the skew of a distribution of scores the lower the value of the standard deviation the higher the value of the standard deviation the lower the value of the range None of the above: measures of dispersion are not affected by skew.
the higher the value of the standard deviation
Which measure of central tendency is affected by every score in the distribution? the mean the median the mode all of the above
the mean
The purpose of measures of central tendency is to describe what value of a distribution of scores is the most typical or representative the most surprising or unexpected the most significant or important all of the above
the most typical or representative
Sixty percent of the respondents in a random sample drawn from a neighborhood are Democrats. The community as a whole is 75% Democrat. The difference between sample and population has been tested and the null hypothesis has been rejected. What may we conclude? Type I error has been committed a one-tailed test has been used the neighborhood is significantly less likely to be Democrat the difference is not significant
the neighborhood is significantly less likely to be Democrat
Comparing one- and two-tailed tests (with a constant alpha level and sample size), the probability of rejection will be higher for the two-tailed test the one-tailed test, if you have correctly predicted the direction of the difference neither, the probability of rejection does not change the test with the most conservative test statistic
the one-tailed test, if you have correctly predicted the direction of the difference
According to the theorems presented in Chapter 6, we can be sure that the sampling distribution is normal if the population is small the population is normal the sample is stratified the sample is normal
the population is normal
The null hypothesis for ANOVA states that the variables are independent the variables are related the population means are equal the population means are different
the population means are equal
An estimator is unbiased if the mean of its sampling distribution is equal to the midpoint of the distribution the sample mean the population value the population median
the population value
As the Critical Region decreases in size -the probability of Type I error increases -the probability of rejecting the null hypothesis increases -alpha increase -the probability of Type II error increases
the probability of Type II error increases
A sample of people attending a professional football game averages 13.7 years of formal education while the surrounding community averages 12.1. The difference is significant at the .05 level. What could we conclude? the null hypothesis should be accepted the research hypothesis should be rejected the sample is significantly more educated than the community as a whole the alpha level is too low
the sample is significantly more educated than the community as a whole
Which of the following must be normally distributed in order to proceed with hypothesis testing of means and proportions? the sample distribution the sampling distribution the population distribution both the sample distribution and the population distribution
the sampling distribution
The Central Limit Theorem states that as sample size becomes large the sampling distribution of sample means approaches normality the sampling distribution of sample means becomes larger the population distribution becomes normal the sample distribution becomes normal
the sampling distribution of sample means approaches normality
While ignoring the independent variable, we make 78 errors when predicting the dependent variable. When taking the independent into account, we reduce the number of errors to 43. Therefore the variables are not associated the variables are associated the independent variable is definitely a cause of the dependent variable phi will be 0
the variables are associated
In a research study conducted to determine if arrests were related to the socioeconomic class of the offender, the chi square critical score was 9.488 and the chi square test statistic was 12.2. We can conclude that the variables are independent being in a certain socioeconomic class causes arrests the variables are dependent the probability of getting these results by random chance alone is 0.5.
the variables are dependent
Unlike other tests of significance, Chi square easily handles situations in which the variables of interest have more than two categories or scores the variables of interest have less than two categories or scores variables are all ordinal in level of measurement degrees of freedom exceed 100
the variables of interest have more than two categories or scores
In terms of the Wheel of Science, an hypothesis is derived from _________ and leads to ___________. statistics, observation theory, generalizations observation, generalizations theory, observation
theory, observation
Which of the following combinations would result in a Type I error? The null hypothesis is actually _______ and our decision in Step 5 is to ________ the null hypothesis. false ... fail to reject false ... reject true ... fail to reject true ... reject
true ... reject
A random sample of 500 reports an average yearly income of $42,000 with a standard deviation of $1000. An estimate of the parameter at the 95% level is about $175 wide. In this research situation we can be 95% confident that the population mean is 42,000 ± 175 the sample size is much too small to justify the use of estimation procedures the alpha level is 1000 the sample mean is $175
we can be 95% confident that the population mean is 42,000 ± 175
When is the t distribution used instead of the Z distribution to test the significance of the difference between two sample means? never when sample size is very large when one sample is much larger than the other when N is small
when N is small
The ANOVA test uses means and standard deviations to compare the amount of variation ______________ with the amount of variation ______________ . within categories ... between categories above categories ... below categories within sample means ... between sample means within sample standard deviations ... between sample standard deviations
within categories ... between categories
If the slope (b) is zero, the value of r would also be zero would be 1.00 would be - 1.00 cannot be determined from the information given
would also be zero
