Psych 311 - Exam #1 Multiple Choice

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.

The sample variance is:

- an unbiased estimator of the population variance - associated with n - 1 degrees of freedom - computed by dividing SS by df

The mode is an appropriate measure of central tendency for

- data that are bimodal - use with other measures of central tendency - data that are on a nominal scale

Discrete values

A variable for which there are no possible values between adjacent units on a scale.

You are interested in measuring the construct, reinforcement. Which of the following measures for this construct is quantitative and continuous?

the size of a reward in grams

A consultant ranks the five most needed areas of improvement for a local business. What scale of measurement are the rankings?

ordinal

The mean is an appropriate measure of central tendency for

- data that are normally distributed - data that are on an interval or ratio scale - data in which the mean, median, and mode are equal

The median is an appropriate measure of central tendency for

- data that are positively skewed - data that are negatively skewed - data that are on an ordinal scale

Measures of variability can range in value from

- ∞ to + ∞

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)

Regardless of the number of scores in a distribution, the range only includes ___ score(s) in its calculation.

10

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 = 1,000. Assuming that a sample of 11 participants was observed in this study, what is the standard deviation for these data?

10 seconds

A researcher decides to split scores on an exam into quartiles. She determines that a score of 64 is at the 25th percentile, a score of 74 is at the 50th percentile, and a score of 80 is at the 75th percentile. What is the interquartile range (IQR) for these data?

16

A researcher computes the computational formula for SS, as finds that ∑x = 39 and ∑x2 = 271. If this is a sample of 6 scores, then what would SS equal using the definitional formula?

17.5

A researcher reports that 12 persons in a sample of 60 reported getting between 4 and 6 hours of sleep per night. What is the relative percentage for this interval?

20%

A researcher selects a sample of 6 males and 11 females. She asks participants to rate the likelihood they would do female-stereotyped jobs (such as nursing or school teaching) on a scale from 1 = not likely at all to 5 = very likely. Men indicated that they would be less likely to do these jobs (M = 2.1) compared with women (M = 4.3). What is the weighted mean for this entire sample of 17 participants?

3.5

Discrete variables

A variable for which there are no possible values between adjacent units on a scale

A researcher computes the computational formula for SS, as finds that ∑x = 22 and ∑x2 = 126. If this is a sample of 4 scores, then what would SS equal using the definitional formula?

5

A researcher computes the definitional formula for SS, as finds that ∑(x-M) = 112. If this is a sample of 20 scores, then what would the value of population variance be using the computational formula?

5.6

A researcher records the sound (in decibels) during a series of lessons taught by a substitute teacher at a local elementary school. In his study, he found that the sound was 80±6 (M±SD) decibels. Assuming the data are normally distributed, which of the following is an appropriate conclusion?

95% of classes were between 68 and 92 decibels.

Which of the following is consistent with the empirical rule? - 68% of all scores lie within one standard deviation of the mean. - 95% of all scores lie within two standard deviations of the mean. - 99.7% of all scores lie within three standard deviations of the mean.

All of the above

A researcher reports that the time (in minutes) it takes children who are "picky eaters" to finish their vegetables is negatively skewed, with children finishing their vegetables in 4.2±1.0 (M±SD) minutes. Based on Chebyshev's theorem, we can conclude that

At least 89% of children finished their vegetables in 1.2 to 7.2 minutes.

A researcher records the number of children at a local school from single-, divorced-, and married-parent homes. This frequency data would be best displayed as a

Bar chart

A researcher records the following scores on a working memory quiz for two samples. Which sample has the largest standard deviation? Sample A: 2, 3, 4, 5, 6, 7, and 8 Sample B: 4, 5, 6, 7, 8, 9, and 10

Both samples have the same standard deviation.

Ratio scales

Contain an absolute zero point that represents the absence of the variable being measured.

Which of the following is an example of a distribution with NO variability? A) scores: 3, 5, 4, 4, 5, and 3 B) scores: 3, 3, 3, 3, 33, and 3 C) scores: 1, 2, 3, 4, 5, and 6 D) scores: 5, 5, 5, 5, 5, and 5

D

Which of the following is NOT a characteristic of the mean? - Add a score above the mean and the mean will increase. - Add a score below the mean and the mean will decrease. - Delete a score below the mean and the mean will increase. - Delete a score above the mean and the mean will increase.

Delete a score above the mean and the mean will increase.

________ is the variable that is believed to change in the presence of the independent variable.

Dependent variable

Ordinal scales

Involve the use of real numbers designating real amounts that reflect relative differences in magnitude.

A researcher records the following data: 4, 4, 4, 4, and 3. How would you describe the variability of these data?

It is very small (close to 0) because scores are approximately the same.

A researcher records the following data for the time (in seconds) it takes five rats to cross an electrical grid to obtain reinforcement on the other side: 12, 9, 13, 4, and 12. Is the mean equal to the mode in this example?

No; the mode is larger than the mean.

Nominal scales

Non numerical names or categories, qualitative, not quantitative.

A researcher distributes frequencies into the following intervals: 1-10, 11-20, 21-30, 31-40, 41-50, and 51 and above. What is wrong with this frequency distribution?

One interval is an open class.

The correct order of operations in math, is:

PEMDAS

A researcher compares the amount of college debt (in dollars) that undergraduate students incur up to their four-year degree. College debt is on what scale of measurement?

Ratio

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

A researcher records the number of classroom interruptions during each of two class sessions. Which session has the largest standard deviation? Session A: 12, 15, 18, 24, and 30 Session B: 8, 10, 12, 16, and 20

Sample A

Descriptive statistics

The goal is to describe or characterize our data

Inferential statstics

The goal is to draw infferences about a population using the data from a sample estimation of sample data applied to a population.

A researcher distributes frequencies into the following intervals: 3-6, 7-10, 11-15, 16-18, 19-22, and 23-26. What is wrong with this frequency distribution?

The interval width is unequal.

A researcher reports that "the average shopper in the sample (n = 12) purchased $65.00 worth of items (μ = $65.00) during a busy shopping day." What mistake was made is this citation?

The sample mean is written using the wrong notation.

A professor grades 120 research papers and reports that the average score was an 80%. What do we know about the sum of the differences of these 120 scores from their mean of 80%?

The sum of the differences is equal to zero.

Which of the following statements about a weighted mean is true. - The weighted mean is always equal to the arithmetic mean. - The weight mean can only be reported id the sample size is equal in each group. - The weighted mean is used to compute the combined mean for two or more samples of scores in which the number of scores in each sample is disproportionate or unequal. - The weighted mean is heavier than an arithmetic mean.

The weighted mean is used to compute the combined mean for two or more samples of scores in which the number of scores in each sample is disproportionate or unequal.

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

A researcher wants to determine how many participants will take less than 24 seconds to complete a cognitive performance task. If he constructs a frequency distribution for these data, what type of distribution would be most appropriate to answer his question?

a cumulative frequency distribution from the bottom up

Continuous Variables

a variable that can have an infinite # of values between adjacent units on a scale

Continuos variables

a variable that can have an infinite # of values between adjacent units on a scale.

The degrees of freedom for the sample variance

are equal to the sample size minus one

What terms refer to each of the following measures, respectively: mean, median, and mode.

average, middle, and most

A simple frequency distribution

can be used to summarize grouped data, can be used to summarize ungrouped data, summarizes the frequency of scores in a given category or range

Adding the same constant to each score in a distribution (or subtracting the same constant from it) will

cause the mean to change by that constant

Qualitative data varies by ________; quantitative data varies by ________.

class; amount

Based on the following graphical summary display, what research design was used to record and analyze these data?

correlational

The scale of measurement a researcher uses

determines the type of inferential statistics that can be done

A researcher selects a sample of 24 participants and has them complete a survey on dating preferences. In this example, what are the degrees of freedom for sample variance and what does this figure represent?

df = 23; it represents the number of scores that are free to vary in a sample.

Each of the following are interval scale measurements, except

duration of sleep (in hours)

The definitional formula ______ the computational formula for SS.

equals

Statistical analysis allows researchers to

evaluate scientific observations

Which of the following research designs is used to determine the causes of behavior that help to explain why the behavior occurs?

experimental

The three steps for constructing a simple frequency distribution are

find the real range, find the interval width, and construct the frequency distribution

A therapist observes that spouses are more likely to forgive their partners for lying to them if they find out the truth from their spouse and not a third party. In this example, the dependent variable is

forgiveness

Which of the following requires the calculation of a real range? A) frequency distributions for categorical B) frequency distributions for ungrouped data C) frequency distributions for grouped data D) frequency distributions that do not use real data

frequency distributions for grouped data

When cumulating frequencies from the top down, the data are discussed in terms of

greater than, at or above, at least

Interval scales of measurement

have equidistant scales

A graphical display for grouped frequency distributions with continuous data is called a

histogram

Which of the following is a type of graphical display used to summarize quantitative, continuous data?

histogram, frequency polygon, ogive

A researcher asks participants to estimate the calories they consume in a meal. The researcher records the following estimates: 450, 426, 310, 500, and 220. If the researcher removes the estimate of 220 (perhaps because the participant drops out of the study), then the value of the mean will

increase

Procedures that allow researchers to infer or generalize observations made with samples to the larger population from which they were selected best describes

inferential statistics

The range of scores in each interval of a grouped frequency distribution is called the

interval width

In the stem-and-leaf display, each number to the right of the vertical line is referred to as a ________; the numbers to the left of the vertical line are called the ________.

leaf; stem

The ________ is the middle value in a distribution of scores that are listed in numeric order.

median

The sum of the squared differences of scores from their mean is

minimal

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

The ________ is the value that occurs most often or at the highest frequency in a distribution.

mode

The variance and standard deviation can never be

negative

A researcher distributes frequencies into the following classes: absent, tardy, present. What type of data are distributed?

nominal data, qualitative data, ungrouped data

A characteristic (usually numeric) that describes a population is called a

population parameter

A psychologist reviews her notes for all her patients and determines that on average her patients complete therapy in 24 days. The average time to complete therapy among all her patients is called a(n)

population parameter

Three key elements of control that allow researchers to draw cause-and-effect conclusions are

randomization, manipulation, and comparison/control

To construct a pie chart, first distribute the data as

relative percentages

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____ (Hint: Calculate the mean first!)

remain the same

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

A characteristic (usually numeric) that describes a sample is called a

sample statistic

The mathematical term ∑x is the numerator for

the population mean, the sample mean

Which of the following distributions has the largest variability? - scores: 1, 3, 6, 9, and 12 - scores: 22, 24, 26, 28, and 30 - scores: 2, 3, 4, 5, and - scores: 1, 2, 3, 4, and 5

scores: 1, 3, 6, 9, and 12

Descriptive statistics are procedures used to

summarize a set of scores or observations, organize a set of scores or observations, make sense of a set of scores or observation

A researcher records 52 scores. What is the median position of these scores?

the average of the 26th and 27th scores in numeric order

Bar charts are a lot like histograms, except

the bars displayed in the graph do not touch

You are interested in measuring the construct, work expertise. Which of the following measures for this construct is quantitative and discrete?

the number of employees that work under an employee

Which of the following measures of attraction is an example of a ratio scale measurement?

the physical proximity (in feet and inches) between two romantic partners

A student scores in the 80th percentile on an exam. What does this mean in comparison to all other students?

the student scored higher than 80% of all others who took the exam

An interquartile range removes

the top and bottom 25% of scores in a distribution before calculating range

A percentile point is

the value of a score on a measurement scale below which a specified percentage of scores in a distribution fall

All other things being equal (so assuming that the value of SS never changes), as sample size increases,

the value of sample variance decreases

The ________ is an arithmetic mean of a weighted or disproportionate set of scores.

weighted mean

When would a researcher calculate a population mean?

when data are measured for all members of a population

Each deviation in the numerator for variance is squared because

without squaring each deviation, the solution for SS would be zero