stats homework questions
10. 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.
7. 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.
6. Two researchers (A and B) compute a one-sample t test. For both tests, the mean difference between the sample and value stated in the null hypothesis is 5, but the standard error is smaller for Researcher A. Which test is more likely to result in a decision to reject the null hypothesis?...
Researcher A
11. Which of the following is true about the computational formula for variance
The computational formula will always produce the same solution as the definitional formula (give or take rounding errors). It is a short-cut method for calculating variance when the population or sample size is large. It is derived mathematically from the definitional formula.
11. All other things being equal, as the degrees of freedom increase, what happens to the critical value for a related samples t test (or for any t test, for that matter)?...
The critical value decreases.
13. A research assistant determines that the distribution of scores in a population is negatively skewed. What effect will this have on the distribution of sample variances?...
The distribution of sample variances will be positively skewed.
5. Which of the following statements regarding the null hypothesis is true?...
The null hypothesis always makes statements about a population parameter.
14. Which of the following is an assumption for computing the related samples t test?...
The population being sampled from is normally distributed. The population variance of difference scores is unknown. Samples are related or matched between groups, but not within groups.
12. A psychologist finds that the population of scores is not normally distributed however, his sampling distribution of the sample means selected from the population are normally distributed. Which characteristic of sampling distributions explains the phenomenon?...
The sample mean follows the central limit theorem.
2. Which of the following explains why point estimation can be a useful procedure to estimate a population mean?...
The sample mean is both equal to the population mean on average and is an unbiased estimator of the population mean.
8. A researcher reports that stress levels among nurses are higher compared to stress levels in the general population, t(20) = 2.086, p = 0.05 (d = 0.12). Was this a one-tailed or a two-tailed test?...
Two-tailed test because the p value is equal to .05
5. 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.
8. A researcher records the following data for the number of different food items chosen by seven participants in a buffet-style setting: 1, 6, 2, 5, 4, 3, and 7. Is the mean equal to the median in this example?...
Yes
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.
1. 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
10. The sampling distribution of the mean and the sampling distribution of the variance (when dividing SS by n − 1)...
are both unbiased estimators
15. The sample variance is an unbiased estimator of the population variance...
both when dividing SS by df and when dividing SS by n ñ 1
6. A researcher reports that the mean difference in response time to an auditory versus a visual cue is 0.83 seconds, with a pooled sample variance equal to 2.45. What is the effect size for this test using estimated Cohen's d?...
d = 0.53; medium effect size
12. The median is an appropriate measure of central tendency for...
data that are positively skewed, data that are negatively skewed and data that are on an ordinal scale
1. Computing a two-independent sample t test is appropriate when...
different participants are assigned to each group, the population variance is unknown and participants are observed one time
6. Which of the following is the denominator of the test statistic for the related samples t test?...
estimated standard error for difference scores
11. Which type of error is used to compute the confidence interval for two independent samples selected from at least one population with an unknown variance?...
estimated standard error for the difference
10. A statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter is called...
estimation
10. The repeated measures design, but not the matched-pairs design, is associated with greater power to detect an effect compared with the independent samples design
false
14. The estimation formula for the two-independent sample t is M1 − M2 ± t(SMD)...
false
15. The estimation formula for the related samples t is MD ± t(SM1 − M2)...
false
1. A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called...
hypothesis testing
4. If the value stated by a null hypothesis is ________ the confidence interval, then the decision would have likely been to retain the null hypothesis...
inside
2. In hypothesis testing, a researcher's decision...
is based on a probability, depends on the level of significance for a hypothesis test and can be to retain or reject the null hypothesis
5. The sum of the squared deviations of scores from their mean...
is computed the same for samples and populations, is computed by squaring each deviation to avoid a zero solution in the numerator and is the numerator for the sample variance and population variance
8. It happens to be the case that the standard error of the sampling distribution of sample means...
is minimal
The range, a measure of variability,...
is the difference between the largest (L) and smallest (S) value in a list of scores, is the most informative when used to describe data sets without outliers and includes only two values in its computation, regardless of the number of scores in a distribution
4. Which of the following is a type of related samples design in which different participants are actually observed in each group, but treated statistically as if they are the same persons in each group?...
matched samples design
13. A researcher records the time (in seconds) that participants arrive late for a scheduled research study. Assuming these data are normally distributed, which measure of central tendency is most appropriate to describe these data?...
mean
6. The ________ is the sum of all scores (in a sample or population) divided by the number of scores summed...
mean
9. Based on the effect size conventions, d = 0.60 is a...
medium effect size
10. The ________ is the value that occurs most often or at the highest frequency in a distribution...
mode
14. A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals. She finds that 2 different hospitals had the highest overall rates of hospital admissions. Which measure of central tendency did this researcher use to describe these data?...
mode
7. The variance and standard deviation can never be...
negative
14. A researcher records a sample of 30 exam scores and finds that the population variance for these data is larger than the sample variance. Is this possible?...
no, the sample variance will be larger because SS is divided by degrees of freedom in the denominator of the variance formula
7. A researcher reports a significant mean difference in a given population. If she computes both eta-squared and omega-squared to measure the effect size, then which estimate will be the most conservative?...
omega-squared
8. A researcher measures mean health scores of children at a local school and compares these scores to the mean health score known in the general population. Assuming that the population variance is unknown, what type of t test is appropriate for this study?...
one-sample t test
2. One difference between a repeated measures design and a matched samples design is that...
only one design involves observing the same participants in each group
3. 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
11. 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
1. The proportion or fraction of times an outcome is likely to occur is referred to as...
probability
3. The denominator of the test statistic for a related samples t test...
provides an estimate of the error associated with the difference scores
13. A professor compares scores on a competency exam among students at two times during a single semester. What type of t test is most appropriate for this study?...
related samples t test
5. A researcher conducts a study in which different participants are independently observed within groups, and the same participants are observed between groups. If there are only two groups, then what type of t test is appropriate for this study?...
related samples t test
11. A researcher asks participants to estimate the height (in inches) of a statue that was in a waiting area. The researcher records the following estimates: 40, 46, 30, 50, and 34. If the researcher removes the estimate of 40 (say, due to an experimenter error), then the value of the mean will...
remain the same
1. A type of related samples design in which participants are observed more than once is called a...
repeated measures design
13. If the null hypothesis is inside the confidence interval, then the decision was likely to ________ using hypothesis testing...
retain the null hypothesis
6. A researcher measures the number of trials it takes two samples of participants to master a new task. In both samples, SS = 240. Sample A consisted of 12 participants and Sample B consisted of 18 participants. Which sample is associated with the largest variance?...
sample A
4. If a portion of people from a population are asked to complete an assessment, then the average score among that group of people would be considered a...
sample mean
5. Which type of mean is used to describe a portion of individuals in a given population?...
sample mean
2. What values are distributed along the x-axis for a sampling distribution of the sample variance?...
sample variances
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
1. The ________ is an inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or mean difference stated in the null hypothesis...
t statistic
What is the implication for the tails of a normal distribution being asymptotic?...
that extreme scores are possible in a normal distribution
4. 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 sample and participants are replaced after being sampled
2. To compute a two-independent sample t test, a researcher has to know many values. Which of the following is NOT a value that the researcher must know to compute this test?...
the pooled population variance
9. A reason for squaring deviations to compute SS in the numerator includes which of the following?...
the sum of the differences of scores from their mean is zero. The sum of the squared differences of scores from their mean is minimal. Squaring scores can be corrected easily by square rooting.
10. All other things being equal (so assuming that the value of SS never changes), as sample size increases...
the value of sample variance decreases
7. For the related samples t test, assuming that all other values remain constant, then as samples size increases...
the value of the test statistic increases, the power to detect an effect increases and the estimate for standard error decreases
7. A researcher obtains z = 2.04 for a one-sample z test. What is the decision for this test at a 0.05 level of significance?...
to reject the null hypothesis
5. 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 0.05 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
6. Given the following values: μ = 6.0, M = 7.6, n = 36, σ = 6, conduct a one-sample z test at a 0.05 level of significance. For a one-tailed test, upper-tail critical, what is the decision?...
to retain the null hypothesis
8. A researcher obtains z = −6.45. What is the decision for a one-tailed test, upper-tail critical, at a 0.05 level of significance?...
to retain the null hypothesis
14. The null hypothesis and alternative hypotheses are statements about parameters in the population...
true
15. The alpha level is basically the same thing as the p value...
true
15. The formula for a population and sample mean only differ by notation; otherwise, these formulas are calculated the same...
true
16. The estimation formula for the one-sample t is M ± t(SM)...
true
A sample mean is not always equal to a population mean...
true
Most behavioral phenomena are believed to approximate the normal distribution...
true
The mean, median, and mode are all located at the 50th percentile in a perfect normal distribution...
true
10. A researcher determines that their critical value is ±1.895 when α = 0.10. Based on this information, is the researcher conducting a one- or two-independent sample t test and what are the degrees of freedom for this test?...
two-independent sample t test, df = 7
3. A researcher records the following data for the number of dreams recalled during a night of sleep for 10 college students: 3, 2, 4, 4, 3, 1, 1, 0, 2, and 0. Is the mean equal to the median in this example?...
yes
9. A researcher records the level of attention among 18 students during an interactive and lecture portion of a single class. If she computes a related samples t test at a 0.05 level of significance (two-tailed test), then what is the critical value for this test?...
±2.110
9. A researcher conducts a two-independent sample t test. He determines that the degrees of freedom is 5. Assuming α = 0.05, what would the critical value be?...
±2.571
A gambler rolls a 3 with one roll of a single fair die. Given that the die was six-sided, what was the probability of rolling a 3 with one roll?...
⅙
13. A researcher wants to conduct a one-independent sample z-test where H0: μ = 33, H1: μ < 33. To do this she determines that the level of significance is α = 0.001. What will be the critical values for this one-independent sample z-test?...
−3.09
8. What are the degrees of freedom for the related samples t test?...
(nD − 1)
1. Measures of variability can range in value from...
0 to +∞
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?...
0.1660
4. A researcher records the following data for the number of bids made on a sample of items sold at an auction. Based on the table, what was the probability that an item had 7 bids made on it?... Number of Bids Frequencies 3 5 4 12 5 7 6 6 7 10
0.25
2. 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
2. A researcher records the following scores for an Olympic gymnast following her routine: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8. What is the range for the scores?...
1.0 (9.9 to 8.9)
12. Given the following values: MD = 19, nD = 10, SS = 1,759, how many standard deviations will the mean shift above or below the unstated population mean difference?...
1.36
6. 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
5. For her study (n = 25), a researcher estimates the 95% confidence interval for a sample with the mean of M1 − M2 = 8.4 and an estimated standard error for the difference SM1 − M2 = 2.2. What will be the lower and upper confidence limits for this interval when conducting a two-independent sample t test?...
3.85, 12.95
8. A researcher computes the definitional formula for SS, and finds that Σ(x − M) = 44. If this is a sample of 12 scores, then what would the value of sample variance be using the computational formula?...
4.0
12. In a sample of 18 participants, a researcher estimates the 80% CI for a sample with a mean of M1 − M2 = 8.8 and an estimated standard error for the difference (SM1 − M2) of 1.8. What is the lower confidence limit for this interval?...
6.4
A researcher records the time in seconds it takes a sample of participants to walk alone through a dark portion of campus. The researcher computes SS = 1,200. Assuming that a sample of 25 participants was observed in this study, what is the standard deviation for these data?...
7.1 seconds
14. In a sample of 20 participants, a researcher estimates the 95% CI for a sample with a mean of M = 5.4 and an estimated standard error (SM) of 1.6. What is the upper confidence limit for this interval?...
8.8
15. In a sample of 12 participants, a researcher estimates the 80% CI for a sample with a mean of M = 22.3 and an estimated standard error (SM)of 4.7. What is the confidence interval at this level of confidence?...
80% CI 15.9, 28.7
13. In a sample of 14 participants, a researcher estimates the 90% CI for a sample with a mean of M1 − M2 = 10.7 and an estimated standard error for the difference (SM1 − M2) of 2.9. What is the confidence interval at this level of confidence?...
90% CI 5.5, 15.9
11. A researcher reports with 90% confidence that 31% to 37% of Americans believe in ghosts. What is the point estimate for this interval?...
34%
4. 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 0.05.
7. It is most appropriate to report effect size with a significant result. Why is it generally inappropriate to report effect size with insignificant results?...
Because it makes little sense to report the size of an effect that you just concluded doesn't exist.
12. A researcher records the following motor assessment scores for two samples of athletes. Which sample has the largest standard deviation? Sample A: 8, 10, 12, 15, and 18, Sample B: 16, 18, 20, 23, and 26...
Both samples have the same standard deviation
9. Which measure of effect size is most commonly reported with a t test?...
Cohen's d
15. A main disadvantage of computing a range is that it is a simple and quick measure of variability...
False
13. A researcher measures the amount of coffee consumed by college students while studying during the final exam week. In her study, she found that students drink 2.3±0.8 (M±SD) cups of coffee per study session. Assuming the data are normally distributed, which of the following is the most appropriate conclusion?...
Most students drink between 1.5 and 3.1 cups of coffee per study session.
12. A researcher reports the following result for a one-sample z test at a 0.05 level of significance: z = 1.88, p = 0.06 (d = 0.25). Is this result significant?...
No, the decision is to retain the null hypothesis.
3. A researcher has participants rate the likability of a sexually promiscuous person described in a vignette as being male (n = 20) or female (n = 12). The mean likability ratings in each group were 4.0. If the null hypothesis is that there is no difference in likability ratings, then do likability ratings differ at a 0.05 level of significance?...
No, this result is not significant, t(30) = 0.
7. A researcher records the following data for the number of times an interviewer is interrupted during a series of interviews: 0, 0, 3, 2, 5, 3, 0, 8, 0, 2, 1, and 1. Is the mode equal to the median in this example?...
No; the median is larger than the mode.
3. Which of the following is NOT a characteristic of probability?...
Probability is most useful for describing fixed events.
12. A researcher concludes that stress levels are higher following a major versus a minor traffic accident (95% confidence interval [CI] 1.86-3.02). If the null hypothesis stated that there would be no difference (null hypothesis: µ = 0), then what is the effect size for this confidence interval?...
Ratings of stress shifted between 1.86 and 3.02 points in the population.
3. A researcher conducts two t tests. Test 1 is a two-tailed test with a smaller sample size at a 0.05 level of significance. Test 2 is a two-tailed test with a larger sample size at a 0.05 level of significance. What do you know about the degrees of freedom for each test?...
Test 2 is associated with larger degrees of freedom.
2. A researcher reports, "the average patron (n = 22) in a local bar consumed more than twice the number of drinks (per day) on weekends (M = 5.4 drinks) compared to weekdays (M = 2.3 drinks)." Although not stated directly, how do we know that the patrons in this study constitute a sample, and not a population of patrons at this local bar?...
The notation for both a sample mean and a sample size was used.
3. A researcher computes a test statistic and finds that the p value for this test is 0.03. What does this result mean?...
There is a 3% likelihood of obtaining the test statistic value, if the null were true.
9. The following samples were selected by two researchers. Which is associated with a smaller standard error of the mean? Researcher A: n = 25, μ = 5, σ = 7 Researcher B: n = 25, μ = 32, σ = 7...
They both have the same standard error.
Most behavior is believed to ________ a normal distribution...
approximate
11. The mean of the sampling distribution of sample means is...
equal to the population mean
In a normal distribution, 50% of all data:..
fall above the mean fall below the median fall above and below the mode
1. Which of the following is not a symbol used with samples...
µ
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
4. A professor teaches a certain section of material using a lot of examples with sports and cars to illustrate. He is concerned that this may have biased his instruction to favor male students. To test this, he measures exam grades from this section of material among women (n = 10) and men (n = 10). The mean score in the male group was 84 ± 4.0 (M ± SD); in the female group, it was 78 ± 8.0 (M ± SD) points. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis at a 0.05 level of significance...
Exam scores were significantly higher in the male group, t(18) = 2.12, p <0.05.
9. A researcher measures the mean time (in seconds) it takes two groups of children to complete an activity task. She finds that Group A (M = 22 seconds) completed the task more quickly than Group B (M = 36 seconds).She then computes a weighted mean for both groups combined and calculates = 26. Based on the information provided, which group had a larger sample size?...
Group A