stats quizzes
A researcher wondered if his new relaxation training method would result in better than average results in helping people to stop smoking. He recorded the average number of cigarettes smoked for his 25 patients six months after undergoing the relaxation training program and compared this to the national average for all smoking cessation programs. Given a two-tailed test, which of the following represents the alternative hypothesis for this scenario?
H1: μ1 ≠ μ2
It is known that the mean weight of the population of newborn infants is 7.4 pounds with a standard deviation of 1.1 pounds. Your sister Tina just had a baby boy who weighed in at 5.4 pounds. How does the weight of your new nephew compare to that of newborn infants in general?
He is 1.82 standard deviations less than the average weight of the population.
Leo is interested in the effects of sleep deprivation usage on number of calories consumed. He asks a group of 20 college students to spend the night in the sleep lab under one of the following conditions: no sleep, 2 hours of sleep, 4 hours of sleep, 6 hours of sleep, or 8 hours of sleep. Leo measures how many calories are consumed by the students in the sleep lab, which is stocked with various food items. After collecting the data, Leo performs an ANOVA and finds that he can reject the null hypothesis. On the basis of this, what does Leo know?
He knows that there is a difference among the groups somewhere, but he does not know where.
Bernie believes that taking vitamins increases IQ. He recruits 36 participants to take vitamins each day and then measures their IQ scores one year later. He calculates a z statistic based on his data and finds that the value of the z statistic is 2.1. Using a two-tailed test and a p value of 0.05, what should he conclude?
He should reject the null hypothesis and conclude that the group who took vitamins had higher IQ scores than would have been expected by chance alone.
Jen designs an experiment in which students are randomly assigned to one of three different study conditions and then are given an exam. She recruits volunteers by handing out flyers in the cafeteria. What assumption of ANOVA does her study violate?
Her sample was not randomly selected.
Why are pictorial graphs typically only used in popular magazines and not scientific journals?
Pictorial graphs are eye-catching but they are often misleading and distracting.
Carra conducts a study and the resulting effect size is small. She decides to replicate the study with a larger sample size. All else being equal, what should she expect to happen to the effect size?
The effect size will stay the same.
What is one important reason for looking at visual descriptions of the data such as frequency?
The patterns revealed in the data may lead to more specific research questions.
Another way of thinking about variability is as the:
amount of spread in the distribution.
As sample size increases, the distribution of scores in the sample:
approaches the shape of the distribution of scores in the population.
A group of students graph the number of gold medals won by each country during the Olympics. What type of graph should they use and what should the y-axis include?
bar graph; the number of gold medals won
The _____ lie refers to using evaluation scales that encourage a particular type of response—for example, by including more positive than negative options.
biased scale
You pick up a copy of Pop Psychology Weekly and notice a big graph on the cover that is displaying the results of a recent happiness survey. The graph indicates that almost everyone answered "very" when asked "How happy are you?" However, survey respondents were only given the options of "extremely," "very," or "somewhat" when answering the question. You are concerned that the graph may be misleading because of the _____ lie.
biased scale
Which of the following techniques for misleading with graphs involves using survey items that do not include the full range of possible responses—resulting in information that is slanted in a particular direction?
biased scale lie
A _____ effect occurs when some constraint prevents a variable from taking values above a certain point.
ceiling
A negatively skewed distribution is more likely to occur whenever we have a:
ceiling effect.
Any unnecessary, distracting information on a graph can be referred to as:
chartjunk.
Which type of variable could theoretically include an infinite number of possible values between any two consecutive numbers?
continuous
If I collect exam grades from the 175 students I teach in introductory psychology, the BEST strategy for finding patterns in the data would be to:
create a frequency table so that I could easily see how many students fell into each grade category.
Central tendency is an example of a(n):
descriptive statistic.
Unnecessary and distracting features of a graph, such as fancy fonts or excessive use of pictures, are often referred to as:
ducks.
A frequency distribution that is bell-shaped, symmetric, and unimodal is called a _____ distribution.
normal
Abraham De Moivre generated a mathematical formula that is the foundation for inferential statistics. We know this formula graphically as the:
normal curve.
If the results from an intelligence test are different when the same person takes the test on two different occasions, the test is:
not reliable.
In a within-groups research design:
participants experience all conditions of the study.
The percentile rank is the:
percentage of scores falling at or below a particular raw score.
Identify the shape of the distribution of the following scores: 16, 15, 92, 15, 20, 25, 95, 20, 25, 20, 24, and 21.
positively skewed
A private high school wants to show that students' test scores are superior to those of students in another school in the district. The administration creates a bar graph showing a very tall bar representing the private school's mean test score and a very low bar representing the mean score for the other school. What part of the graph would show if the private school is exaggerating the difference between schools?
range of values on the y-axis
Daniela asked students in her introductory psychology class to report their majors. Her data list was as follows: psychology, psychology, psychology, sociology, psychology, criminal justice, psychology, education. In this example, the individual, untransformed reports of major are:
raw scores.
An insurance company hires Ulric to explain car accidents that are the result of people who are looking at the road while driving but do not see an oncoming car, a type of accident labeled as "driver looked but did not see." Ulric creates an experiment in which participants see two pictures flashing on a computer screen. Both pictures show what looks to be the same scene but one is slightly different. Ulric records how long it takes people to notice the change (reaction time) and how many sets of pictures they view during a 5-minute session. What should Ulric include on a scatterplot to most effectively describe these data?
reaction time and number of pictures viewed
When constructing graphs, it is best to include the zero value on both axes whenever practical because it:
reduces the likelihood of misinterpreting the data.
If we reject the null hypothesis, our result is said to be:
statistically significant.
Bar graphs are highly informative, but they can also be deceiving because what seems to be a significant difference in means may actually be a small difference. What part of the graph reveals if a difference in means is exaggerated?
the range of values on the y-axis
. In the famous Zimbardo prison study, a group of Stanford students were assigned to be either a prisoner or a guard so that the experimenters could examine prison life behaviors and interactions. The experiment was intended to run for two weeks but was stopped after only six days because of the brutal behavior of the guards and the depression of the prisoners. What was the independent variable in this study?
the role of prisoner or guard
A nurse at a local hospital records the number of male babies and the number of female babies born during the month of August. Should he create an ungrouped or grouped frequency table to represent the data?
ungrouped, because there are only two values on the x-axis
In a hypothesis test, a z statistic that is less extreme than the critical values indicates that:
we don't have enough evidence to support the research hypothesis.
Hypothesis testing tells us:
what are significant results, but does not indicate anything about the importance of those results.
Under what conditions is it permissible to proceed with a hypothesis test, even though the assumption that participants are randomly selected is violated?
when you are cautious about generalizing your results
The F statistic increases when:
within-groups variance decreases and between-groups variance increases.
A(n) _____ provides frequency information about words in a given context.
word cloud
When the confidence interval is 95 percent, the critical values of z that we should use are:
±1.96.
The standard deviation of a population is symbolized by:
σ.
Yolanda examined the GRE math scores of the second-year graduate students in her statistics class to see the variability. She found the variance to be 1600. What is the standard deviation?
40
You are conducting an independent-samples t test with 22 participants in each of two groups. What is the degrees of freedom for this problem?
42
he z, t, and F distributions have something in common—that the denominator of the test statistic:
contains a measure of sample variability.
Our ability to reject the null hypothesis given that the null hypothesis is false is:
statistical power.
Professor Taylor recently administered a psychology exam and was surprised to see that the distribution of scores was positively skewed. For this example, a positively skewed distribution indicates that:
most students did poorly on the exam but a few did very well.
With very few degrees of freedom, the test statistic:
needs to be more extreme to reject the null hypothesis.
A distribution containing a few extremely small values is likely to create a distribution that is:
negatively skewed
Identify the shape of the distribution of the following scores: 25, 26, 22, 27, 26, 26, 29, 30, 21, 22, and 4.
negatively skewed
If we asked 100 people how much they like pizza we would probably find that most people like it a lot with only a few people saying they don't like it at all. That is, the distribution of scores would be:
negatively skewed.
Discrete observations include both:
nominal and ordinal variables.
A bar graph is appropriate if your independent variable is _____ and your dependent variable is _____.
nominal; scale
A researcher measures the amount of food consumed by each dog in her lab. She finds that the mean amount eaten by the 16 dogs is 12 oz. The sum of squared deviations is 192. What is the standard deviation for this data set?
3.46
If we know the percentage of scores falling between the mean and a z score of +0.98 is 33.65 percent, then what is the percentage of scores falling between the mean and a z score of -0.98?
33.65 percent
A graduate statistics class is unhappy with midterm grades. The professor will curve the grades only if the class figures out how much the curve needs to be in order for the mean score to equal 85. What should the curve for the class be if these are the midterm scores for class members: 72, 88, 95, 76, 69, 71, 81, 80, 73, and 85?
6 points
Experiments are usually preferred to correlational studies because they:
have the ability to establish cause-and-effect relationships
Identify the correct formula for using the sample standard deviation to estimate the population standard deviation.
√((Σ(X - M)2)/(N - 1)
3. The mean mathematics score for college-bound seniors who took the SAT in 2013 was 514. If the standard deviation for this same year was 118, what is the z score for a person who received an SAT mathematics score of 650?
+1.15
Given a population mean of 7.2, a sample mean of 8.7, and standard error of 0.50, calculate the single-sample t value.
+3.00
In a study designed to test the results of cramming versus spaced practice, the researcher finds that students who crammed scored an average of 72 on the exam, while students who spaced out their practice scored an average of 78 on the exam. If the value of sdifferenceis 2.5, what is the value of t?
-2.4
Carson keeps track of the number of dinner guests at his home each night for one week. The data set is as follows: 12, 12, 12, 12, 12, 12, 12. What is the standard deviation of the scores?
0
In a paired-samples t test, the null hypothesis posits that the mean of the comparison distribution is:
0.
When calculating variance, the mean of the deviations is always equal to:
0.
What proportion of a normal distribution corresponds to z scores greater than +1.02?
0.1539
In a one-way, repeated-measures ANOVA, SSbetween = 49.5, SSwithin = 115, and SSsubjects = 39.1. What is the value of R2?
0.30
The quantitative subtest of the Graduate Record Exam (GRE) has a mean of 500 and a standard deviation of 100. A sample of 100 students take the GRE and have an average quantitative score of 503. What is the value of the z statistic that corresponds to the sample mean?
0.30
Approximately 96 percent of scores fall within ____ standard deviation(s) of the mean.
2
A researcher is interested in the amount of time students spend on social networking sites. She obtains a sample of 10 students and records the amount of time (in minutes), in one day, they spend on Facebook, Instagram, or Twitter. Assume that the following summary information is from her data: N = 10, μ = 47.7, SS = 2000. What is the variance for this example?
200
Thomas decides to use the mode as the measure of central tendency for his map study. What is the mode in his data set: 13, 27, 22, 15, 14, 26, 27, 22, 17, 27, 15, and 13?
27
Based on the information in the source table below, find the F. Source SS df MS F Between-groups 405.2 3 135.07 Within-groups 175.5 36 4.875 Total 580.7 39
27.71
Given a mean difference score of 15 and a standard error of 5, what is the value of the paired-samples t test statistic?
3
Imagine that you calculated Body Mass Index (BMI) for a group of college students and created the grouped frequency table shown below: BMIFrequency 40-44.99 1 35-39.994 30-34.99 6 25-29.9910 20-24.9920 15-19.993 If you decide to depict this data with a histogram, what would be the midpoint for the first interval?
42.5
For the scores 9, 8, 4, 2, 3, 6, the mean is:
5.33.
It is known that the mean weight of the population of newborn infants is 7.4 pounds with a standard deviation of 1.1 pounds. What is the weight (in pounds) of a newborn infant with a z score of +0.87?
8.36 pounds
Dr. Choi is examining the weights of 750 children, ages 2 to 18, to find out if childhood obesity rates are increasing in his city. With this type of data, is it better to use a frequency table or a grouped frequency table and why?
A grouped frequency table is better because Dr. Choi is working with a large data set of continuous intervals.
In which of the following situations would it be necessary to use a between-groups ANOVA?
A researcher is interested in whether a sexual harassment training class changes attitudes toward sexual harassment. The researcher assesses these attitudes before and after the training class.
Assume that the average age at which men get married in Orange County is normally distributed with a mean of μ = 29.8, σ = 5 (fictional data). (a) What percentage of the married men in Orange County were married between the ages of 31 and 35? (b) What percentage of the married men in Orange County were married before they were 24? a) 25.60 percent; (b) 12.30 percent.
A. 25.6% B. 12.30%
Which of the following pieces of information is NOT needed when calculating power?
All of these are needed to calculate power.
Steve scored a 77 out of a possible 100 on his midterm calculus examination. The distribution of the class had a mean of 68 and a standard deviation of 8.8. A friend of Steve's who is in a different calculus class scored a 78 out of a possible 100. His class distribution had a mean of 68 and a standard deviation of 16. Relative to the performance of their classes, who did better? Steve's z score: (77 - 68)/8.8 = 9/8.8 = 1.02. His friend's z score: (78 - 68)/16 = 10/16 = 0.63. Although both scored relatively well and above the class averages, Steve performed better on the calculus exam relative to his friend.
Even though, Steve's friend scored higher on the test, Steve scored higher than 84.61% of his class. While his friend scored only 73.57% better than his class.
What does it mean that the normal curve is symmetric?
Exactly 50 percent of scores fall below the mean and 50 percent fall above the mean.
The results of an independent-samples t test are reported in a scientific journal as: t(14) = 1.14, p > 0.05. What decision was made?
Fail to reject the null hypothesis.
Ken's F value associated with the between-groups difference is 4.25. His dfbetween = 3 and dfwithin = 10. Assuming an alpha level of 0.01, what should he conclude?
Fail to reject the null hypothesis. The calculated value does not exceed the critical value.
If the critical q value from the table is 4.5, which of the following group differences would be significant?
HSD (group 2 vs. group 3) = -6.5
Suppose we are interested in examining the social aspects of eating behavior. Twenty participants are placed in a room with various types of snack foods and are told to eat whatever they like while they are waiting for the researcher. Ten of the participants wait alone while the other 10 wait with 2 other people. The research hypothesis in this experiment is that when participants wait with others, they will eat less food than when they wait alone. If we fail to find a difference between the two groups, which of the following might be true?
Our small sample size may have resulted in low statistical power and thus made it more difficult to reject the null hypothesis.
The measure of effect size calculated for ANOVA is:
R2.
Yun wants to calculate the median in a set of scores, but there are two middle numbers. How should she determine the value of the median?
Report the average of the two middle scores.
In a journal article, the standard deviation would be symbolized as:
SD.
In the R2 formula for a one-way within-groups ANOVA, _____ is the variability caused by differences among participants.
SSsubjects
Barbara calculates a single-sample t-test and obtains a value of 2.05. Her sample size was 5, and she used a one-tailed test with an alpha level of 0.05. What should she conclude?
She should fail to reject the null hypothesis. The critical value is larger than the calculated value.
Which of these is NOT an assumption of the one-way, repeated-measures ANOVA?
The cases in one group are independent of the cases in another group.
Which of these is NOT an assumption of the z test?
The distribution of the sample is normal.
A local police chief is giving a presentation to the city council about speeding violations. She constructs a grouped frequency table showing the number of tickets issued for different speeds over the 30 mile-per-hour limit. Which statement gives the error that she made in constructing the table? SpeedFrequency 50-59.992 45-49.993 40-44.996 35-39.9917 30-34.991
The intervals are not equal.
The first step in calculating the median is to:
arrange the scores in ascending order.
Which of the following refers to a single score in a distribution of scores?
X
Sun is reading an article about autism rates and how they are increasing in a majority of Western countries around the world. She notices that the authors incorrectly used a line graph to depict the number of autism diagnoses among five different countries, which is a nominal variable. What type of graph should have been created to represent the autism rates in different regions of the world?
bar graph
As the size of the effect of the independent variable increases, power tends to:
increase.
The comparison distribution in a paired-samples t test is a distribution of:
mean difference scores.
In a distribution that is positively skewed, most of the scores occur ______ of the distribution.
on the left side
A residential neighborhood of several modestly priced homes is undergoing a transformation. Recently, a few very expensive homes have been built in the area. If we created a frequency distribution of home values in the neighborhood, what would it look like?
positively skewed
Imagine that you calculated Body Mass Index (BMI) for a group of college students and created the grouped frequency table below: BMIFrequency 40-44.991 35-39.994 30-34.996 25-29.99 10 20-24.9920 15-19.993 If you decide to depict this data with a histogram, what values would appear on the x-axis?
the frequency of each interval
In computing variance and standard deviation we are interested in how much individual scores vary from:
the mean.
Which of the following provides a measure of practical importance?
the measure of effect size d
Joline is a kindergarten teacher who is interested in calculating the variability in the number of sight words remembered by the 32 students in her class. What is the best measure of variability in this situation?
the standard deviation, because it uses all of the scores in the data set and is easy to interpret
For the one-way within-groups ANOVA, we calculate _____ F statistics, but we are only interested in _____.
two; one
The graph in your text comparing the cost of higher education with the quality of education at Cornell University was used to illustrate:
ways that graphs can be misleading.
One advantage of standardization is that:
we can make meaningful comparisons of variables measured on different scales.
Bernie believes that taking vitamins increases IQ. He recruits 36 participants to take vitamins each day and then measures their IQ scores one year later. The mean IQ score for his participants is 102. If the population mean for IQ scores is 100 with a standard deviation of 15 points, which of the following provides the z statistic for his data?
(102 - 100) / (15/36)
Samantha compares her class's average score on a standardized statistics exam (M = 43) to the known national population mean for the same exam (μM = 44). The standard deviation based on her class (N = 36) is 1.2. If she wants to conduct a t test, which of the following is the correct formula?
(43 - 44)/(1.2/√36)
A z score of _______ is equivalent to the 16th percentile.
-1
Given a pooled variance value of 1.43, with 10 participants in one group and 8 in the other, what is the value of s2difference
0.32
It is known that in 2013 the population mean for the writing section of the SAT is 488, with a standard deviation of 114. A sample of 400 students taking the SAT whose family income was between $60,000 and $80,000 had a writing score of 496. (a) Perform a one-tailed hypothesis test to determine whether this group scored significantly higher on average than the population. (b) Assume that rather than a sample of 400, the sample size was only 20. Perform the same hypothesis test again with this new sample size. Does the conclusion differ from what was found in (a)?
1) There is no significant difference between the two populations, therefore we fail to reject the null hypothesis. 2) The conclusion does not differ, but the z-statistic does get smaller. (a) The calculated z statistic, z = 1.40, does not exceed the cutoff value of +1.65 (one-tailed hypothesis test, using a p level of 0.05). Therefore, we fail to reject the null hypothesis. The writing SAT score of students with a family income between $60,000 and $80,000 was not significantly greater than that of all students who took the SAT. (b) If the sample size is only 20, the standard error changes from 5.70 to 25.49. If we use the sample size of 20 to calculate the z statistic, z = 0.31, and the critical value of +1.65 is not exceeded, we would still fail to reject the null hypothesis. This conclusion does not differ from that reached when the sample size was 400.
In a study designed to assess the impact of stress on performance of a new task, 17 participants were assigned to the stress condition and 15 were assigned to the control condition. Assuming a one-tailed test and an alpha level of 0.05, what is the critical value?
1.698
Given the following scores, calculate the mean of the difference scores.Participant #BeforeAfter1120125212112431211224119117
1.75
A researcher wondered if his new relaxation training method would result in better than average results in helping people to stop smoking. He recorded the average number of cigarettes smoked for his 40 patients immediately before undergoing the relaxation training program and again six months after completing the program. The degrees of freedom for this test is:
39.
Which of the following techniques for misleading with graphs involves the selection of people to participate in a study so that the results turn out a certain way?
sneaky sample lie
Statistical power is related to:
the probability of not making a Type II error.
Mehl (2007) published a study in the journal Science reporting the results of an extensive study of 396 men and women that compared the number of words uttered per day by each sex. If Mehl was testing the idea that women talk more than men do, the null hypothesis for the study would be _____ and the research hypothesis would be _____ (in symbolic terms).
H0: µ1 ≤ µ2; H1: µ1 > µ2
A New York Times article published on April 24, 2007, reported the research of Dr. Giorgio Vallortigara, a neuroscientist at the University of Trieste, Italy, and his two colleagues. The researchers asked whether a dog wags its tail in a preferred direction in response to positive stimuli and in another direction in response to negative stimuli. To answer their question, they recruited 30 dogs that were family pets. Filming each dog from above, they allowed it to view (through a slat in its cage) three positive stimuli separately, in order of descending positivity: its owner, an unfamiliar human, and a cat. All the dogs responded by wagging their tails to the right. But when the dogs were presented with an unfamiliar, aggressive dog, a negative stimulus, all dogs wagged their tails to the left. Which of these is the null hypothesis for this study?
A dog's tail wagging will be the same in response to positive stimuli as to negative stimuli.
A team of employees at a restaurant franchise uses a grouped frequency table to show the number of items sold at different price points in a given week. Which statement gives the error that they made in constructing the table? Cost (in dollars)Frequency 8-9.99 0 6-7.9925 4-5.9965 2-3.9975 0-1.9914
The table only needs to include highest to lowest values.
The state lottery association reports that the mean lottery winner wins $1,000,000. Why should you be suspicious of this report?
You suspect that most lottery winners win a small amount, but that a few individuals who win a large amount unduly influence the mean.
Which of the following would be the best operational definition of happiness?
a participant's rating of happiness on a scale of 1-5
The denominator of the ratio for calculating the paired-samples t statistic is the:
estimated standard error of the distribution of mean difference scores.
Juanita bought a chain of video rental stores in the late 1990s and business was very strong for a couple of years. The number of video rentals was increasing yearly and she was very confident that the increase would continue indefinitely. However, she did not foresee the rise of video-on-demand and consequently her business has been in a slow decline for the past several years. Juanita's assumption that the upward trend in video rentals would continue could be referred to as a(n):
extrapolation lie.
Statistical methods that use sample data to draw inferences about larger populations are called ________ statistics.
inferential
One of the ways that graphs may mislead is by assuming that some value between the data points lies on a straight line between those data points. This is referred to as the _____ lie.
interpolation
A measure is said to be valid if:
it measures what it is supposed to measure.
By convention, an R2 value of 0.16 would be considered:
large
Including chartjunk on your graph is not advisable because it:
makes it difficult to interpret your data.
If our data are nominal, we should use _____ as a measure of central tendency.
mode
Alexander asks his classmates to identify as either full-time students or part-time students. Since his data is nominal, the best measure of central tendency is the:
mode.
A researcher wants to learn about the vocabulary of two-year-olds. She measures the number of words for 300 two-year-old children. The group of 300 children is an example of a(n):
sample.
Although researchers primarily study _____, they are more interested in _____.
samples; populations
A histogram is used with _____ data.
scale
A(n) _________ variable meets the criteria for either an interval variable or a ratio variable.
scale
Michael wants to graph the relation between scores on the SAT and first semester grade point average in college. What type of graph should he use?
scatterplot
Effect sizes rely on comparison of a distribution of _____ rather than on a distribution of _____ and are therefore unaffected by sample size.
scores; means
Assuming critical values of -2.306 and +2.306 for an independent-samples t test, if we obtain a calculated t value of -2.30, we:
should fail to reject the null hypothesis.
A newspaper article reported that the typical American family spent an average of $81 for Halloween candy and costumes last year. A sample of N = 16 families this year reported spending a mean of M = $85, with s = $20. What statistical test would we use to determine whether these data indicate a significant change in holiday spending?
single-sample t test
Bob is conducting a research project examining the effects of sexist commercials on men's attitudes toward women. He has two groups of men watch either a sexist commercial—with women cleaning houses and acting unintelligent—or a progressive commercial portraying women in a powerful role. After they watch the commercial the men will answer some questions designed to assess their attitudes toward women. Bob's instructor feels that his research does not have sufficient statistical power. What could Bob do to increase power?
strengthen the effect of the independent variable by having the men watch several sexist commercials (rather than just one) or several nonsexist commercials
A post-hoc test is warranted when:
the F is significant and we have more than two groups.
Unnithan, Houser, and Fernhall (2006) were interested in whether playing the game Dance Dance Revolution (DDR) affected the heart rate of overweight adolescents differently than it did non-overweight adolescents. Twenty-two adolescents, 10 classified as overweight and 12 as not overweight, played DDR for 12 minutes while the researchers measured each participant's heart rate. On average, the researchers found no difference between the heart rate of the two groups. The research hypothesis for this study is that
the heart rate of the overweight group and the non-overweight group will differ after both groups play Dance Dance Revolution.
