Exam 1 CH. 1-7
A relative percent distribution is often used instead of a relative frequency distribution because:
most readers find it easier to understand percentages than decimals
When a weighted mean is computed for two or more samples with unequal sample sizes, which value is used as the weight in the formula?
n
The only difference in computing sample and population variance is that the SS is divided by ______ for the sample variance.
n-1
Experimental research is typically conducted using a sampling strategy in which
the same participant can never be selected twice in the same sample
What is the z score for scores in the lowest 2.5%?
-1.96
A sample of 25 participants where the population mean was 10 and standard deviation of 5 completed a word recall test. What is the probability of obtaining a sample mean that is at least two standard deviations larger than the population mean?
.0228
Scores on a board game were: 23 3.1 (M SD) points. Assuming these data are normally distributed, what is the probability that a competing team got 20 points or less?
.1660
A sample of 144 participants from a population with a mean of 100 and a variance of 36 completed a cognitive test. What is the standard error of the mean?
0.5
The z distribution is normally distributed with a mean of 0 and a variance of ____.
1
A researcher determines that employees at a company commuted an average of 90 (+/- 30) minutes per week. Assuming these data are normally distributed, what is the z score for an employee commuting 60 minutes per week?
1.0
If the smallest score in a distribution is 12 and the largest is 71, then what is the interval width if we create 6 intervals?
10
A researcher found that a group of rats took 18±2 minutes (M±SD) to learn a route to find a reward. How long did it take 80% of the rats to learn the route?
19.68 minutes.
If the smallest score in a distribution is 10 and the largest is 32, then what is the real range for these data?
23
As a general rule, when the number of intervals needed to summarize a data set is smaller than ____, we can leave the data ungrouped.
5
Using the computational formula to compute SS for a specific array of values, . If this is a sample of 4 scores, then what would SS equal using the definitional formula?
5
A swimmer measures the time it takes for each of his laps and determines that a time of 15 seconds is at the 25th percentile, a score of 17 seconds is at the 50th percentile, and a score of 21 seconds is at the 75th percentile. What is the interquartile range (IQR) for these data?
6
A psychologist records the time in seconds it takes a sample of children to complete a set of problems, and computed the SS = 1600. Assuming that the psychologist observed a sample of 25 children in this study, what is the variance and standard deviation for these data?
66.7; 8.2
A researcher states that a sample of 100 babies from a rural area weighed 25 ± 7.5 (M ± SEM) pounds at their first birthday. Which value is the standard error of the mean?
7.5
A researcher records M = 12 in a sample of men (n = 10) and M = 8 in a sample of women (n = 20). What is the weighted mean for these samples?
9.33
Which of these statements is false?
A researcher can directly control the probability of a Type II error
On average the sample mean will equal the population mean, and the sample mean is an unbiased estimator.
True
One step to hypothesis testing is to compute the test statistic.
True
Random assignment is not possible in a quasi-experiment because the variables being studies cannot be manipulated.
True
The alpha level is completely different from the p value.
True
The definitional formula for the standard deviation requires that you know the value of the mean.
True
The greater the power, the more likely we are to correctly reject the null hypothesis, if it is incorrect.
True
The larger the population standard deviation, the larger the standard error of the mean will be.
True
The range takes into consideration only two values regardless of the number of scores in a distribution.
True
The interquartile range (IQR) is the range of a distribution of scores
after the top 25% and bottom 25% of the scores in that distribution are removed
The mean is used to describe:
all of the above (data that are normally distributed, interval scale data, ratio scale data)
If a researcher selects a sample of 36 participants from a population with a variance of 16, then the standard error of the mean will be 2.0.
False
In an ordinal scale, a larger number represents a greater value than a smaller number, and the ratio of any two numbers represents a meaningful value.
False
The standard error is the sample variance divided by the square root of the sample size.
False
The variance is the best estimate of variability since it takes into account all values except the mean.
False
In blinded studies, consumers' rankings of the effectiveness of brand name painkillers did not differ from generic painkillers that had the same key ingredients, on a 5-point scale. The scale used in these studies is
An Interval scale
According to the central limit theorem, as the number of samples in the sampling distribution increases, the sampling distribution of sample means selected at random from that population will
Approach the shape of a normal distribution.
Is children's vocabulary related to their parents' education level? To answer this, researchers measured the number of words 3-year-old children knew, and their parents education (in number of years). This data can be examined using:
Correlational method
The mean for a vocabulary test is 100; a researcher selects a sample to administer this test. In this example, the null hypothesis is
D
A librarian at a university is interested in looking at how many undergraduate students use the library. He records student use of different library resources and tabulates this usage. This information is an example of
Descriptive statistics
Students were asked to rate the effectiveness of video lectures for an online class. Their ratings on a 5-point scale would be
Discrete and quantitative
A researcher records the number of songs played by a station in one hour on weekdays, with commercial interruptions. In his study, he found that the average number of songs played, the M = 16, and standard deviation = 3. Assuming the data are normally distributed, which of the following is an appropriate conclusion?
During weekdays 95% of the time, the station played between 22 and 10 songs per hour..
The SS in two similar experiments was found to be 104. Experiment 1 had 10 participants and experiment 2 had 20 participants. Which experiment is associated with the largest variance?
Experiment 1
Randomly assigning to different groups to ensure that manipulations of the independent variable are measured on similar groups is necessary in:
Experimental method
A Type III error is possible for hypothesis tests where the rejection region is located in both tails.
False
A sampling distribution is a distribution of all population means or variances that could be obtained in samples of a given size from the same population.
False
A z score for the mean in a normal distribution is always equal to 1.
False
All z scores above and below the mean are positive.
False
An effect size of d = 0.18 is a large effect in the population.
False
Descriptive statistics can help to infer the unknown parameters in a population.
False
High School GPA and score on the SAT exams are considered during college admissions. Both these values are continuous and quantitative measurements.
False
A librarian at a university is interested in looking at how many undergraduate students use the library. He records student use of different library resources in one month and extrapolates this information for the year-round usage. This is an example of
Inferential statistics
A researcher records the following data: 10, 10, 10, 10, and 10. How would you describe the variability of these data?
It is equal to zero because scores are the same.
Data from airline passengers were ranked by their country of origin, an example of a
Nominal scale
Listeners to a specific radio station were asked to rank one hundred songs for popularity. The composite rank score for the songs were then published, and shows use of a
Ordinal scale
A librarian at a university is interested in looking at how undergraduate students use the library resources. He sends a survey about the library usage to all undergraduate students in the college but receives responses from only a subset of students. In this example, the librarian was interested in getting information from the ______________, but could obtain only a _____________.
Population; sample
Which of the following is a characteristic of probability?
Probability varies between 0 and 1.
A researcher studies the development of cognitive flexibility by testing children of different age groups on a problem-solving task. This is an example of a:
Quasi-experimental method
In one study it was reported that scores were lower than the population mean, and z = -1.75, 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
The power in hypothesis testing is
The probability of rejecting a false null hypothesis
Of these, the largest proportion in a z distribution could be:
The proportion of area that lies between z = +1 and z = -1.
A researcher studying the development of executive functions in children conducts an experiment and computes a test statistic. He finds that the p value for this test is .025. This result means
There is a 2.5% likelihood of obtaining the test statistic value, if the null were true.
A continuous variable is measured along a continuum at any place beyond the decimal point, and can be positive (e.g., height) or negative (e.g., temperature) in value.
True
A researcher selected data that were normally distributed, and appropriately concluded that about 95% of scores occurred between 2 standard deviations below and above the mean.
True
For normal distributions, 95% of data will fall within two standard deviations of the mean.
True
In a normal distribution, the mean can take on positive or negative values.
True
Multiplying or dividing each score using the same constant will change the standard deviation.
True
The median is:
all of the above (the preferred measure of central tendency when outliers are in a data set, the middle value in a distribution listed in numerical order, at the 50th percentile of a cumulative percent distribution )
Scatter grams can be used to illustrate the relationship between ________.
bivariate plots
Scores close to the mean are located in the ________ of a normal distribution.
body
A researcher obtains z = 3.79 for a one-sample z test. If the researcher decided to retain the null hypothesis, then:
both A and B (Their decision was inconclusive.; Their decision was based on a two-tailed test. )
A method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample, is called
both a and b (hypothesis testing; significance testing)
When we sum the frequencies across a series of intervals, the summary is called a:
cumulative frequency distribution
An ogive is used to summarize what type of frequency distribution?
cumulative percent
Which of the following will decrease the value of the mean for a distribution of scores?
deleting an existing score above the mean
A bar chart is similar to a histogram, except that in a bar chart, each rectangle ________ the adjacent rectangles at the boundaries of each interval:
does not touch
A researcher measures a sample mean for five samples. The sample mean in each sample is M = 2, M = 4, M = 5, M = 7, and M = 9. What will the sum of the differences of scores from the mean equal in each sample?
equal to 0
A researcher selects a sample of 49 participants from a population with a standard deviation of 7. What is the standard error of the mean?
equal to 1
Each of the following is a rule for constructing a histogram, except:
frequencies are plotted at the midpoints of each interval and the line connects each plot
It is necessary to create intervals for a simple frequency distribution with what type of data?
grouped data
A researcher measures the distance (in miles) that students travel during a holiday season. What type of graph (shown below) was used to summarize these data? Is it appropriate?
histogram; yes because the data are continuous
A researcher decreases the sample size, which will:
increase the value of standard error
The following are true for sampling without replacement except
it is used in the development of statistical theory
A researcher records the following time (in seconds) that children in a sample play with an unfamiliar toy: 12, 14, 10, 6, 8, 10, 13, 12, 4, 12, and 6. Which measure of central tendency (the mean, median, or mode) is largest?
mode
A researcher measures the following scores: 0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 2, 4, 2, 2, 4, 4, 4, 4, 4, and 0. Should these data be grouped?
no, because the number of different scores is small
The mode is the primary measure of central tendency to describe data on which scale of measurement?
nominal
The mean is the balance point of a distribution, which means that it is:
not always located at the center of a distribution of scores
The median can be used for skewed distributions and ordinal data. Why is the median appropriate for describing ordinal data?
ordinal data convey direction only (more or less than)
If the value of the test statistic is in the rejection region, then
p < .05
Sampling strategy used in developing statistical theory is based on
participants are replaced after being sampled
A ________ is a cumulative percent summary in which the ranks indicate the percent of scores at or below a given value.
percentile rank
A graphical display in the shape of a circle that is used to summarize the relative percent of discrete and categorical data into sectors is called a:
pie chart
The _________ is the sum of N scores divided by N, whereas the ________ is the sum of n scores divided by n.
population mean; sample mean
The variance of the sampling distribution of sample means equals the ______________ divided by the sample size
population variance
The variance and standard deviation can only be
positive
The proportion or fraction of times an outcome is likely to occur is referred to as
probability
A ________ frequency distribution is often used for larger data sets where the number of frequencies in each interval could be in the thousands or millions.
relative
Which of the following distributions has the smallest variability?
scores: 2, 3, 4, 5, and 6
Only one of the following is a step to hypothesis testing
set the criteria for a decision
All of the following are true about normal distributions except
the distribution is asymmetrical
The probability of an outcome or event is
the fraction of times an outcome is likely to occur
The mean for a distribution of scores is M = 6. If we measure a new score equal to 10, then what will happen to the mean?
the mean will increase
Although different symbols are used to represent the number of scores in a sample and population, the computation of central tendency is ________ for samples and populations.
the same
Given the following values: u = 5.0, M = 6.6, n = 25, s (population) = 5, 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
The weighted mean is used to compute the mean for samples with ________ sizes.
unequal
The population mean is identified by the Greek letter ________; the sample mean is identified by an italicized ________.
µ : M