Stats Exam 2
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 seconds 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 category?
.8247
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
The standard normal distribution is normally distributed with a mean of ____ and a variance of ____.
0; 1
A researcher records the following times (in seconds) that it took a group of students to complete an exam: 18±2 minutes (M±SD). How long did it take 80% of students to complete the exam?
19.68 minutes.
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 seconds
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
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
Which of the following is required to locate z scores with a given proportion?
Find the z score associated with a given probability. Compute a z-transformation to find the raw score.
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.
Increasing sample size will
Increase the power of 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.
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.
Which of the following best describes the p value.
It is a conditional probability
Based on the effect size conventions, d = 0.99 is a
Large effect size
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.
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
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
The normal distribution is symmetrical, which means that
scores above the mean are distributed the same as scores below the mean
Hypothesis testing is also called
significance testing
A measure of the size of an effect in a population is called
effect size
Which of the following is not one of the four steps to hypothesis testing?
evaluate the plan
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
In a normal distribution, 50% of all data
fall above the mean fall below the median fall above and below the mode
A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called
hypothesis testing
Based on the effect size conventions, d = 0.60 is a
medium effect size
The following distribution most closely approximates a
normal distribution
A theoretical distribution that evenly distributes data around the mean, median, and mode is called the
normal distribution bell-shaped distribution Gaussian distribution
If the value of the test statistic is in the rejection region, then
p < .05 the decision is to reject the null hypothesis the value of the test statistic is larger than the critical value
The proportion or fraction of times an outcome is likely to occur is referred to as
probability
In hypothesis testing, a researcher can never
prove that his or her hypothesis is correct
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.
standard normal transformation
The first step to hypothesis testing requires that a researcher
state the hypotheses
Scores far from the mean are located in the ________ of a normal distribution.
tails
What is the implication for the tails of a normal distribution being asymptotic?
that extreme scores are possible in a normal distribution
The power of the decision-making process is
the likelihood of rejecting a false null hypothesis
Researchers state a level of significance in terms of an alpha level. The alpha level indicates
the probability of committing a Type I error the probability of incorrectly rejecting the null hypothesis the probability value for the rejection region
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
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
The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a
z score
The probability of committing a Type I error is stated by ________; the probability for committing a Type II error is stated by ________.
alpha; beta
Most behavior is believed to ________ a normal distribution.
approximate
The one-sample z test is a hypothesis test used to test hypotheses
concerning a single population with a known variance
When reporting the results of a one-sample z test using APA format, the ________ does not need to be reported.
critical values
What is the z score for scores in the top and bottom 2.5%?
+ or - 1.96
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 minutes 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 minutes per week?
-1.0
What is the z score for scores in the bottom 10%?
-1.28
What is the z score for scores in the bottom 5%?
-1.645
Which of the following is required to locate proportions of area under the normal curve?
Compute a z-transformation. Find the probability of a z score in the unit normal table.
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.
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 σ = 2.3 and the standard deviation in Population B is σ = 4.3. Which population is associated with the highest power to detect an effect?
Population A
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
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 alpha level in Study 1 was larger than the alpha level used in Study 2. Which study is associated with greater power to detect an effect?
Study 1
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.
Which proportion is largest in a z distribution?
The proportion of area between z = +1 and z = -1.
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 to 8 hours as moderate sleepers. What percentage of participants fell in this category?
about 35%
In hypothesis testing, a researcher's decision
is based on a probability depends on the level of significance for a hypothesis test can be to retain or reject the null hypothesis
The criteria 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
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 9 birdcalls during this experimental session?
.0013
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
μ = 78
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
Which of the following is a possible value for the standard deviation of a normal distribution?
.5
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
.50
A researcher measures the number of tasks completed by participants during a 5-minute 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
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
What is the z score for scores in the top 2.5%?
1.96
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 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.
Is a one-sample z test reported differently for one-tailed and two-tailed tests?
No, the same values are reported.
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.
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 copulation.
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.
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.
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
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.
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 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.
If a researcher obtains a null finding, then what is the decision?
They correctly retained the null hypothesis.
Given the following values: μ = 10, M = 8, σM = 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
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 researcher directly controls for the probability of a ________, but does not directly control for the probability of a ________.
Type I error; Type II error
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
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 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 score for 2 symptoms per day is 0. Assuming the data are normally distributed, did she reach her goal?
Yes, because a z score of 0 is the average, or mean.
________ 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
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 total number (or population) of residents
The total number of possible outcomes for a random variable is referred to as
the sample space
The normal distribution has all of the following characteristics, except that
the total area under the curve is greater than 1.0
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 this characteristic has no practical implication
A professor finds that the average SAT score among all students attending his college is 1150±150 (μ+σ). He polls his class of 25 students and finds that the average SAT score is 1200. 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
Given the following values: μ = 6.0, M = 7.6, n = 36, σ = 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
