Statistics - Exam 2
Which type of sampling is most often applied by researchers in the behavioral sciences?
experimental sampling
A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is ______.
0.50
The standard normal distribution is normally distributed with a mean of ______ and a variance of ______.
0; 1
A researcher has participants choose between three advertisements. She finds that 54 prefer Ad A, 86 prefer Ad B, and 60 prefer Ad C. The probability or proportion of participants preferring Ad B is ______.
43
A researcher records the following assessment data: 42 ± 6 (M ± SD). The researcher only wants to sample participants scoring in the top 20% of this assessment. What is the cutoff score for the top 20% in this example?
47.04
Researchers state a level of significance in terms of an alpha level. The alpha level indicates ______.
all of these
The probability of committing a Type I error is stated by ______ and the probability for committing a Type II error is stated by ______.
alpha; beta
Most behavior is believed to ______ a normal distribution.
approximate
Two normal distributions are observed. The first distribution has a mean of 12 and a standard deviation of 2. The second distribution has a mean of 0 and a standard deviation of 2. For which distribution will the z score for the mean be larger?
None, the z score will be the same
A researcher reports that the standard deviation in Population A is = 2.3 and the standard deviation in Population B is = 4.3. Which population is associated with the highest power to detect an effect?
Population A
A researcher reports that the size of an effect in Population A is d = 0.10 and the effect size in Population B is d = 0.34. Which population is associated with greater power to detect an effect?
Population B
Which of the following is NOT a characteristic of probability?
Probability is most useful for describing fixed events
Two researchers select a sample for a population with a mean of 12.4 and a standard deviation of 9. Researcher A selects a sample of 30 participants. Researcher B selects a sample of 40 participants. Which sample is associated with a smaller standard error?
Researcher B's, because the sample size was larger
A researcher selects two samples of 64 participants each. In the first sample, the population mean was 10 and the variance was 16. In this second sample, the population mean was 25 and the variance was 9. Which sample will be associated with a larger standard error of the mean?
Sample 1
A researcher conducts two studies. Each study was a one-sample z test. Both studies placed the rejection region in both tails and measured the same sample mean. The beat level in Study 1 was larger than the beta level used in Study 2. Which study is associated with greater power to detect an effect?
Study 2
A researcher directly controls for the probability of a ______, but does not directly control for the probability of a ______.
Type I error; Type II error
A researcher randomly selects a sample of participants from a population with a variance of 4. If a researcher selects a sample of 16 participants with a mean of 12, then what is the mean and standard error for the sampling distribution of the mean?
mean = 12, standard error = 0.5
A researcher reports that the size of an effect in some population is d = 0.88. Which of the following is an appropriate interpretation for d?
mean scores shifted 0.88 standard deviations in the population
Based on the effect size conventions, d = 0.60 is a ______.
medium effect size
A professor gives an exam in which the mean score is 78 points. She gives another exam to test whether or not scores change. In this example, the null hypothesis is ______.
mu = 78
A parent decides to reward her child if he eats an average of at least five bites of his vegetables at dinner during the first week. She finds that her child ate 4 ± 0.8 (M ± SD) bites per meal for the first week. Assuming these data are normally distributed, should this parent reward her child?
no, because the z score for 5 bites is greater than 0
A researcher reports the following result for a one-sample z test at a .05 level of significance: z = 1.88, p = -.06 (d = .25). Is this result significant?
no, the decision is to retain the null hypothesis
Is a one-sample z test reported differently for one-tailed and two-tailed tests?
no, the same values are reported
The shape of the sampling distribution of the mean is approximately ______, whereas the shape of the sampling distribution of the variance is approximately ______.
normal; positively skewed
Suppose you select a sample of three people from a population of four (A, B, C, D). Which of the following samples is possible using the experimental sampling strategy?
persons B, C, and D
The proportion or fraction of times an outcome is likely to occur is referred to as
probability
What values are distributed along the x-axis for a sampling distribution of the sample variance?
sample variances
Based on the effect size conventions, d = 0.18 is a ______.
small effect size
A distribution of z scores are distributed in what type of unit of measurement?
standard deviation units
The first step to hypothesis testing requires that a researcher ______.
state the hypotheses
Given the following values: = 10, M = 8, = 0.5, conduct a one-sample z test at a .05 level of significance. What is the decision for a two-tailed test?
to reject the null hypothesis
Given the following values: = 6.0, M = 7.6, n = 36, = 6, conduct a one-sample z test at a .05 level of significance. For a one-tailed test, upper-tail critical, what is the decision?
to retain the null hypothesis
How is the standard error of the mean typically reported in a graph?
using error bars
What is the z score for scores in the top and bottom 2.5%?
+-1.96
What is the z score for scores in the top 2.5%?
+1.96
In a normal distribution, 50% of all data ______.
- fall above the mean - fall below the median - fall above and below the mode
In hypothesis testing, a researcher's decision ______.
- is based on probability - depends on the level of significance for a hypothesis test - can be to retain or reject the null hypothesis
A theoretical distribution that evenly distributes data around the mean, median, and mode is called the ______.
- normal distribution - bell-shaped distribution - Gaussian distribution
What is the z score for scores in the bottom 10%?
-1.28
A researcher records the following number of birdcalls made during an experimental session with robins: 7.2 ± 0.6 (M ± SD). Assuming these data are normally distributed, what is the probability that robins made more than nine birdcalls during this experimental session?
.0013
A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean that is at least two standard deviations larger than the population mean?
.0228
What is the typical level of significance for a hypothesis test in behavioral research?
.05
A researcher records the following response times to a visual stimulus: 23 ± 3.1 (M ± SD) seconds. Assuming these data are normally distributed, what is the probability that participants responded in 20 s or less?
.1660
A researcher records the following body mass index (BMI) scores for a group of participants: 28.4 ± 1.6 (M ± SD). Participants who score between 25 and 30 on this scale are categorized as overweight. What percentage of participants fell in this overweight category?
.8247
A researcher records the following times (in seconds) that it took a group of students to complete an exam: 18 ± 2 min (M ± SD). How long did it take 80% of students to complete the exam?
19.68 min
A researcher selects a sample of size 6 from a population of size 10. How many possible samples of this size can be selected using theoretical sampling?
1,000,000
A researcher selects a sample of 121 participants from a population with a mean of 32 and a standard deviation of 22. What is the standard error of the mean?
2.0
An article states that a sample of 40 participants took 12 ± 2.3 (M ± SEM) s to complete a cognitive assessment. Which value is the standard error of the mean?
2.3
A researcher records the following times (in seconds) that it took a group of mice to complete a maze: 23 ± 4.1 (M ± SD). The top 10% of mice finishing with the fastest times will be placed in a "maze bright" group. What is the cutoff time to be placed in this group?
28.25 s
A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20. About 68% of the sample means in this sampling distribution should be between a sample mean of ______.
36 and 40
A researcher states that a sample of 100 shoppers spend 112 ± 40 (M ± SEM) dollars on groceries each week. Which value is the standard error of the mean?
40
A professor records the following final exam scores: 78 ± 7 (M ± SD). Students scoring in the top 14% get an A. What is the cutoff score for the top 14% in this example?
85.56
A researcher selects a sample of 9 participants from a population with a mean of 8 and a standard deviation of 3. About 14% of the sample means in this sampling distribution should be between a sample mean of ______.
9 and 10
What does it mean to say that the sample mean is an unbiased estimator of the population mean?
If we select a sample at random, then on average we can expect the sample mean to equal the population mean.
What is the central limit theorem?
It explains that a sampling distribution of possible sample means is approximately normally distributed, regardless of the shape of the distribution in the population.
A researcher selects two samples of 25 participants each. In the first sample, the population mean was 32 and the variance was 8. In this second sample, the population mean was 4 and the variance was 8. Which sample will be associated with a larger standard error of the mean?
None, both samples will have the same value for standard error
A researcher selects a sample of 36 students from a school population with a mean IQ of 100 and standard deviation of 12. She determines that the mean IQ in this sample is 104. Assuming she computes a one-sample z test at a .05 level of significance, what is the decision for a two-tailed test?
Reject the null hypothesis; IQ scores in this sample are significantly higher than those in the population.
The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?Researcher A: n = 18, = 8, = 2.4Researcher B: n = 12, = 8, = 2.4
Researcher A
The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?Researcher A: n = 36, = 12, = 9Researcher B: n = 36, = 12, = 6
Researcher B
Which of the following describes the largest proportion in a z distribution?
The proportion of area between z = +1 and z = -1
When a researcher decides to retain the null hypothesis because the rejection region was located in the wrong tail, this is called a ______.
Type III error
A researcher randomly selects a sample of athletes and reports that their average score on a health and fitness scale is 23. Based on the characteristics of the sample mean, what does this say about the mean in the population?
We expect that the population mean is equal to 23 because the sample mean is an unbiased estimator of the population mean.
The following distribution most closely approximates a ______.
a normal distribution
A researcher records the following time spent sleeping per night (in hours) in a group of participants: 5.8 ± 1.8 (M ± SD). The researcher decides to categorize participants who sleep between 6 and 8 hr as moderate sleepers. What percentage of participants fell in this category?
about 35%
Because the sampling distribution of sample means is normally distributed, we can use the ztransformation formula to find probabilities. Which of the following gives the appropriate notation for this formula?
all of these
If the value of the test statistic is in the rejection region, then ______.
all of these
The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n - 1) ______.
are both unbiased estimators
A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean that is at leastequal to the population mean?
both A and B
Which of the following is required to locate proportions of area under the normal curve?
both A and B
Which of the following is required to locate z scores with a given proportion?
both A and B
Regardless of the distribution of the population, the sampling distribution of sample means will be approximately normally distributed. What characteristic of the mean explains this?
central limit theorem
The one-sample z test is a hypothesis test used to test hypotheses ______.
concerning a single population with a known variance
Which of the following is not a step to locate a proportion in a normal distribution?
convert a proportion to a standard normal z score
When reporting the results of a one-sample z test using APA format, the ______ does not need to be reported.
critical values
A researcher increases the sample size, which will ______.
decrease the value of standard error
As sample size increases, the standard error of the mean ______.
decreases
A measure of the size of an effect in a population is called ______.
effect size
______ allows researchers to describe (1) how far mean scores have shifted in the population or (2) the percentage of variance that can be explained by a given variable.
effect size
The mean of the sampling distribution of sample means is ______.
equal to the population mean
A researcher visits a population of 1,200 local residents to determine the proportion of local residents who support a new smoking ban. In this case, the sample space is ______.
equal to the population of 1,200 local residents
A researcher selects a sample of 25 participants from a population with a mean of 10 and a standard deviation of 5. What is the probability of selecting a sample mean equal to at least 12?
equal to the probability of selecting a sample mean that is at most equal to 8
A researcher obtains z = 3.98 for a one-sample z test. If her decision is to retain the null hypothesis, then what do you know about her decision?
her decision resulted in a Type III error
A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called ______.
hypothesis testing
Which of the following is not one of the four steps to hypothesis testing?
identify hypothetical data
Increasing sample size will ______.
increase the power the decision
A researcher conducts a study, but has low power to detect an effect. Which of the following is one way in which the research can increase power?
increase the sample size
It happens to be the case that the standard error of the sampling distribution of sample means ______.
is minimal
A researcher obtains z = 1.80 for a one-sample z test. What is the decision for this test at a .05 level of significance?
it depends on whether the test is one-tailed or two-tailed
The criterion for a decision regarding the value stated in a null hypothesis is set by the ______.
level of significance
A researcher believes that increasing attention given to children will improve mean academic performance. Therefore, the alternative hypothesis should be ______.
mean academic performance will increase
In hypothesis testing, a researcher can never ______.
prove that his or her hypothesis is correct
In Step 2 of hypothesis testing, researchers state a level of significance to minimize the probability of ______.
rejecting a true null hypothesis
What are the two decisions that researchers can make in hypothesis testing?
retain or reject the null hypothesis
What values are distributed along the x-axis for a sampling distribution of the sample mean?
sample means
A researcher selects from a participant pool of four males and six females. He determines that the probability of selecting two male participants is p = .16. Based on this probability, what strategy did the researcher use to sample participants?
sampling with replacement
A researcher selects from a participant pool of four males and six females. He determines that the probability of selecting two female participants is p = .30. Based on this probability, what strategy did the researcher use to sample participants?
sampling without replacement
The normal distribution is symmetrical, which means that ______.
scores above the mean are distributed the same as scores below the mean
Suppose a researcher wants to make sure that the probability of committing a Type I error is less than 5%. How can the researcher control for this?
set the alpha level at .05
Hypothesis testing is also called ______.
significance testing
What is the implication for the tails of a normal distribution being asymptotic?
that extreme scores are possible in the tails of a normal distribution
Which of the following statements regarding the null hypothesis is true?
the null hypothesis always makes statements about a population parameter
A researcher reports that scores were higher than the mean in the population, z = 1.60, p = .05 (d = .14). If this was a test at a .05 level of significance, then what value must be incorrectly reported?
the p value
Experimental research is typically conducted using a sampling strategy in which ______.
the same participant can never be selected twice in the same sample
The normal distribution has all of the following characteristics, except that ______.
the total area under the curve is greater than 1.0
State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 0.80, or the area to the right of z = -0.80.
the two areas are the same
A professor finds that the average SAT score among all students attending his college is 1150 150 ( ). He polls his class of 25 students and finds that the average SAT score is 1,200. Suppose he computes a one-sample z test at a .05 level of significance. What is his decision?
to reject the null hypothesis for an upper-tailed test, but to retain the null hypothesis for a two-tailed test
A researcher obtains z = -6.45. What is the decision for a one-tailed test, upper-tail critical, at a .05 level of significance?
to retain the null hypothesis
A researcher obtains z = 1.45 for a one-sample z test. What is the decision for this test at a .05 level of significance?
to retain the null hypothesis
Which of the following is not a step to locate a score in a normal distribution?
transform a raw score (x) into a z score
A therapist has a goal to reduce the mean number of patient symptoms expressed for a particular disorder to two symptoms per day. Following therapy, she determines that the z scorefor two symptoms per day is 0. Assuming these data are normally distributed, did she reach her goal?
yes, because a z score of 0 is the average, or mean
The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a ______.
z score
A researcher selects a sample of 64 participants from a population with a mean of 10 and a variance of 16. What is the standard error of the mean?
0.5
Which of the following is a possible value for the standard deviation of a normal distribution?
0.5
A researcher selects a sample of size 4 from a population of size 6. How many possible samples of this size can be selected using experimental sampling?
15
A counselor records the number of disagreements (per session) among couples during group counseling sessions. If the number of disagreements is distributed normally as 4.4 ± 0.4 (M ± SD) disagreements, then what proportion of couples disagree at least 4 times during each counseling session?
.8413
A researcher obtains z = 2.04 for a one-sample z test. What is the decision for this test at a .05 level of significance?
to reject the null hypothesis
A researcher measures the number of tasks completed by participants during a 5-min multitasking session. If the number of tasks completed is distributed normally as 6.3 ± 1.0 (M ± SD) tasks, then what is the probability that participants completed less than 8 tasks?
.9554
In terms of characterizing samples, statistical theory was developed using a sampling strategy in which ______.
- the order of selecting participants matters - the same participant can be selected twice in the same example - participants are replaced after being sampled
By definition, the probability of an outcome or event is ______.
- the proportion of times an outcome is likely to occur - the fraction of times an outcome is likely to occur - particularly useful for predicting the likelihood of random events
Which of the following is a scenario in which increasing sample size will increase power ______.
- when the effect size is small - when the effect size is large - when the probability of a Type I error is small
A researcher determines that students are active about 60 ± 12 (M ± SD) minutes per day. Assuming these data are normally distributed, what is the z score for students being active 48 min per week?
-1.0
A researcher determines that students study an average of 80 ± 20 (M ± SD) minutes per week. Assuming these data are normally distributed, what is the z score for students studying 60 min per week?
-1.0
What is the z score for scores in the bottom 5%?
-1.645
A professor finds that the students scored a 76 ± 8 (M ± SD) on the final exam. On this exam, a score of 90 is an A. Assuming these data are normally distributed, what is the z score for 90 (the cutoff for an A)?
1.75
A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for, say, Candidate A equals ______.
1/3
A researcher computes a one-sample z test in two studies. Both studies used the same alpha level, placed the rejection region in both tails, and measured the same sample mean. The researcher selects a sample of 30 participants in Study 1 and decides to retain the null hypothesis. She selects a sample of 60 participants in Study 2 and decides to reject the null hypothesis. Which of the following is the best explanation for why the decision was different in Study 1 and Study 2?
The different decisions in Study 1 and Study 2 are possible because the second test was associated with greater power to detect an effect.
If a researcher obtains a null finding, then what is the decision?
they correctly retained the null hypothesis
A sampling distribution of the sample mean or variance is ______.
a distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population
A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called ______.
a sampling distribution
The ______ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1.
a standard normal transformation
A researcher finds that the average preschool-aged child drinks two cups of milk per day. Assuming these data are normally distributed, the z score for the average cups per day in this example is ______.
exactly equal to 0
Which of the following best describes the p value?
it is a conditional probability
Based on the effect size conventions, d = 0.90 is a ______.
large effect size
A researcher selects a sample of 49 participants from a population with a mean of 12 and a standard deviation of 3.5. What is the probability of selecting a sample mean of 13 or larger from this population?
less than .03
Scores far from the mean are located in the ______ of a normal distribution.
tails
Which of the following allows researchers to use the standard normal distribution to estimate the probability of selecting sample means?
the central limit theorem
State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the left of z = 1.00, or the area to the left of z = -1.00.
the first area is bigger
Each of the following statements are true, except that ______.
the larger the sample size, the larger the standard error
The power of the decision-making process is ______.
the likelihood of rejecting a false null hypothesis
The total number of possible outcomes for a random variable is referred to as ______.
the sample space
State whether the first area is bigger, the second area is bigger, or the two areas are equal: the area to the right of the mean, or the area between z = ±1.00.
the second area is bigger
The mean can take on any value and the standard deviation can take on any positive value. Therefore, ______.
there are an infinite number of possible normal distributions
A researcher computes a test statistic and finds that the p value for this test is .03. What does this result mean?
there is a 3% likelihood of obtaining the test statistic value, if the null were true
The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean?Researcher A: n = 25, = 5, = 7Researcher B: n = 25, = 32, = 7
they both have the same standard error
