CH 6 and 7
The statistical concept of p levels is often referred to as:
alphas
The z-score distribution ________ has a mean of ________.
always; 0
When creating a distribution of means, it is important that whatever scores are sampled to compute the means are:
replaced back into the population for additional sampling.
The term ________ is used for the distribution of means in place of the term standard deviation.
standard error
z scores are useful because they:
give us an understanding of where a score falls in relation to the mean of its underlying population, allow comparisons to be made between scores from different distributions, and permit the transformation of z scores into percentiles.
If most of the participants in a study misinterpret the rating scale they are using, which problem will be present in your data?
misleading data
The ________ forms a symmetrical and mathematically defined bell-shaped pattern.
normal curve
Distributions of scores approach the normal distribution as the:
number of scores increases.
If a distribution of scores has a mean of 55 and a standard deviation of 5, then a score of 70 has a z score that is ________ standard deviation(s) from the mean.
3
Which score is more extreme: 0.32 or -0.45?
-0.45
Jenna scored 40 on a standardized test of reading ability where the mean score is 50 and the standard deviation is 10. Based on this information, what is Jenna's z score?
-1.0
Gibson (1986) asked a sample of college students to complete a self-esteem scale on which the midpoint of the scale was the score 108. He found that the average self-esteem score for this sample was 135.2, well above the actual midpoint of the scale. Given that the standard deviation of self-esteem scores was 28.15, what would the z score be for a person whose self-esteem score was 101.6?
-1.19
The critical value(s) associated with a p level of 0.05 for a one-tailed hypothesis test using the z statistic is (are):
-1.65 or 1.65
The critical value(s) associated with a p level of 0.05 for a two-tailed hypothesis test using the z statistic is (are):
-1.96 and 1.96
Following is a list of z scores from a single distribution of scores. Which of the z scores corresponds to the raw score farthest from the mean of the distribution?
-2.3
The typical probability adopted by researchers to determine whether a result is extreme is:
0.05.
What proportion of a normal distribution corresponds to z scores greater than 1.04?
0.1492
In a normal standard curve, which percentile corresponds to a z score of -1.0?
16
The distribution of means based on samples of size 45, pulled from a population distribution with a mean of 100 and a standard deviation of 15, would have a standard error of:
2.24
If samples have at least ________ scores, the distribution of means will most likely approximate a normal curve.
30
Sample means based on at least ________ scores tend to approximate a normal distribution, even when the underlying population is skewed.
30
Given the properties of the standard normal curve, we know that ________% of all scores fall below the mean and _______% fall above the mean.
50; 50
What are the consequences of succeeding in meeting all the assumptions of a parametric test when performing research?
A research study that meets all the assumptions of the parametric test used to analyze the data produces higher quality results than does a research study that fails to meet some of the assumptions.
The symbol for the null hypothesis is ________, and the symbol for the research hypothesis is ________.
H0; H1
What are the consequences of failing to meet the assumptions of a parametric test when performing research?
If the test is robust to the violation, it does not invalidate the research; it may, however, make it more difficult to detect effects.
Regardless of your decision on how to deal with dirty data, what should you always do?
Report your decisions for other researchers to assess.
Under what conditions do we not meet the assumption that the dependent variable is assessed on a scale measure?
The data are clearly nominal or ordinal.
Which of the following statements is not an assumption of the z test?
The distribution of the sample is normal.
Which of the following statements is NOT an assumption of parametric hypothesis tests?
The sample size is greater than 30.
Two students from two different schools recently took a science test. The first student correctly answered 34 questions on the test and the second student correctly answered 48 questions. What can you conclude from the two students' test scores?
The two students cannot be compared because there was no standardization procedure permitting appropriate comparisons.
The formula for calculating the raw score from a z score is:
X = z(σ) + µ.
The second step in converting a z score into a raw score is:
adding the mean of the population to the product obtained from multiplying the z score and standard deviation.
Because of the principle of ________, when sample sizes are at least 30, the distribution will most likely resemble a normal distribution.
central limit theorem
We rarely have access to an entire population, so we typically calculate the mean of a sample and:
compare that to a distribution of mean by calculating a z statistic.
We reject the null hypothesis when the test statistic falls in which area of the distribution?
critical region
When we calculate a z test, we compare data from our sample to a:
distribution determined by the null hypothesis.
A ________ is composed of means based on samples rather than raw scores.
distribution of means
The second step in calculating a z score is:
expressing the obtained values in standard deviation units.
A z score is a measure of:
how far away from the mean a score is in terms of standard deviations.
As sample size ________, the spread of distribution of means ________.
increases; decreases
Gerber and Malhotra (2006) found an irregularly high spike in published z scores:
just greater than 1.96.
What percentage of scores fall beyond 3 standard deviations away from the mean?
less than 5%
A distribution of means would be more likely to have ________ compared to a distribution of raw scores.
lower variance
If the assumptions of parametric testing are not met, researchers must:
make a decision to continue with parametric or nonparametric tests.
Repeated sampling of ________ approximates a normal curve, even when the underlying population is skewed.
means
The first step in converting a z score into a raw score is:
multiplying the z score by the standard deviation of the population.
Inferential statistical analyses that are not based on a set of assumptions about the underlying population are:
nonparametric tests
Mehl (2007) published a study in the journal Science reporting the results of an extensive study of 396 men and women comparing the number of words uttered per day by each sex. If he was testing the idea that women talk more than men do, what type of hypothesis test would Mehl conduct?
one-tailed test
The percentile is the:
percentage of scores falling at or below a particular raw score.
The process of standardization involves the conversion of raw scores to ________ scores.
standard
Irregular patterns of correct answers shared by multiple students on standardized tests have lead to speculation that:
teachers may have completed tests for students in order to raise performance levels.
The symbol for the standard error is:
σM.
The null hypothesis states that:
there are no differences between the populations being studied.
The formula for z based on the mean of a sample is:
z = (M - µM)/σM.
The formula for calculating a z score is:
z = (Χ - µ)/σ.
When calculating a z score for a distribution of means, we refer to the z score as a:
z statistic.
In a normal standard curve, what percentile corresponds to a z score of 1.0?
84
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. The professor tells Mackenzie she scored at the 44th percentile. How many hours does she study per week?
9.24 hours
What is the percentage of observations that fall between z scores of -1.2 and 0.50?
57.64
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Treating this class as the population, what percent of students study more than 8 hours?
66.28
In a normal standard curve, approximately ________% of scores fall within 1 standard deviation from the mean.
68
When should you consider throwing out the whole data set and starting over?
if the problem is widespread or systematic (a particular group or condition failed to respond)
The statement "It is hypothesized that children who attend an enrichment program will score higher on IQ tests compared to children who do not attend an enrichment program" best illustrates a:
one-tailed test
Which of the following is not a reason data might be misleading?
participants taking their time to understand the items
A single observation can be expressed in a number of ways that all refer to that same observation and the exact same place within the normal curve. These expressions are
raw score, z score, and percentile
When attempting to find a percentage associated with a z score, the first step involves a ________ to ________ transformation.
raw score; z score
Because of ________, skewed distributions approximate normal curves when means are based on larger samples.
the central limit theorem
According to ________, as sample size increases, the distribution of ________ assume a normal shape.
the central limit theorem; sample means
When hypothesis testing, a more common and conservative approach is to use a ________ rather than a ________.
two-tailed test; one-tailed test
A ________ is a distribution of z scores.
z distribution
A ________ represents the number of standard deviations a particular score is from the mean average.
z score
We reject the null hypothesis only when:
the p value associated with our test statistic is smaller than the p level we have chosen.
The statement "It is hypothesized that men and women will differ on reaction time measures" best illustrates a:
two-tailed test
If a variable is measured on a nominal scale, the assumption that the ________ should not be made.
variable is measured on a scale
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Treating the class as the population, what is the percentile for a student in the class who studies 10 hours a week?
50.8
The mean for the population is 80 with a standard deviation of 5. Given a z score of 1.45, what is the raw score?
87.25
The mean for the population is 67 with a standard deviation of 8.78. Given a z score of 2.56, what is the raw score?
89.48
In a normal standard curve, approximately ________% of scores fall within 2 standard deviations from the mean
96
Imagine that the mean height for all Division I women's basketball programs is 69 inches with a standard deviation of 3 inches. The 2010-2011 women's basketball team at the University of Connecticut, with 10 players listed on the roster, had an average height of 71.2 inches. Using the z statistic, what percent of means would fall below that for these UConn Huskies?
98.98%
The first step in calculating a z score is calculating:
the difference between a particular score and the population mean.
A person with a z score of zero would have a raw score equal to:
the mean of the distribution of raw scores.
The phrase statistically significant means that:
the research result was unlikely to have occurred by chance.
The statement, "It is hypothesized that participants in a stress condition will perform significantly different than participants in a control group on a series of memory tasks," best illustrates a:
two-tailed test
Assume the average height for American women is 64 inches with a standard deviation of 2 inches. What percent of groups of size 25 would have mean heights of more than 64.5 inches?
10.56%
Daniel wanted to know his approximate score on the final exam for his mathematics class. His professor hinted that his score was well above the class average. The professor announced that the mean for the class final exam was 90 with a standard deviation of 7. Given Daniel's z score of 1.67, what is the raw score for Daniel's exam grade?
101.69
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Jessica is working two jobs and struggles to find time to study, averaging only 3 hours per week. What percent of students are at least as extreme as Jessica, in both directions?
12.86
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. The professor tells David he scored at the 76th percentile. How many hours does he study per week?
13.14 hours
If we know that the percentage of scores falling between the mean and a z score of 0.40 is 15.54, then what is the percentage of scores falling between the mean and a z score of -0.40?
15.54
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Mark studies 16 hours per week. What percent of students are at least as extreme as Mark, in both directions?
18.02
Adam scored 70 on his final exam. His class's average score was 50, with a standard deviation of 10. What is Adam's z score?
2
On the first statistics exam, the class average was 70 with a standard deviation of 6. You scored 82. What is your z score?
2
________ requires that all members of a population have an equal chance of being selected for a study.
Random selection
A distribution of scores has a mean of 20.2 with a standard deviation of 0.89. Compare a score of 21.6 with a z score of 1.2?
The z score of 1.2 is greater, resulting in a raw score of 21.27.
Under what conditions is it permissible to proceed with a hypothesis test even though the assumption that the population distribution is approximately normal is violated?
We have a sample size greater than 30.
When attempting to find a percentage associated with a z score, the second step involves looking up
a z score on the z table
To compare a group mean to a population, compute:
a z statistic.
The mean of the distribution of a set of z scores is:
always 0
Two students recently took algebra class tests. The students are at different schools but wanted to compare their performance. The first student scored 80 on the test. Her class average was 90 with a standard deviation of 10. The second student scored 70. Her class average was 50 with a standard deviation of 10. Which student did better?
second student because she performed better relative to her class
The distribution of means has the same mean as the distribution of scores for the population, and the spread is:
smaller
To convert a person's percentile rank into a raw score, you need to know the mean and:
standard deviation for the population.
The z distribution is a normal distribution of:
standardized scores.
If we reject the null hypothesis, the result is said to be:
statistically significant.
The symbol for the population mean is:
µ.
Adam scored 70 on his final exam. His class's average score was 50, with a standard deviation of 10. How many standard deviations is Adam's score from the mean?
2 standard deviations above the mean
According to the 2003-2004 annual report of the Association of Medical and Graduate Departments of Biochemistry, the average stipend for a postdoctoral trainee in biochemistry was $31,331 with a standard deviation of $3,942. What would be the z score of a trainee making $42,566?
2.85
If a distribution of scores has a mean of 90 and a standard deviation of 10, then a score of 70 has a z score that is ________ standard deviation(s) ________ the mean.
2; below
If we know that the percentage of scores falling between the mean and a z score of 0.50 is 19.15, then what is the percentage of scores falling below a z score of -0.50?
30.85
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Treating this class as the population, what percent of students study more than 12 hours a week?
32.28
________ are the requirements that the population from which we are sampling has specific characteristics that will allow us to make accurate inferences.
Assumptions
Under what conditions is it permissible to proceed with a hypothesis test even though the assumption that participants are randomly selected is violated?
We are cautious about generalizing the results.
What is the difference between the denominator of the equation for the z score and that of the z statistic?
When computing a z score, we divide by the population standard deviation, but when computing a z statistic, we divide by the standard error of the sampling distribution.
Three problems that can lead to contaminated or "dirty" data are:
missing data, misleading data, and outliers.
To determine a person's percentile, you first need to convert the person's raw score to a
z score
If we wished to compare two scores that are measured on different scales, we would need to transform the scores into:
z scores.
The z distribution is equivalent to a distribution of:
z scores.
Assume the average height for American women is 64 inches with a standard deviation of 2 inches. What percent of groups of size 25 would have mean heights of less than 62 inches?
zero percent
The symbol for the population standard deviation is:
σ.
In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Treating this class as the population, what is the percentile for a student in the class who studies 8 hours a week?
33.72
In a raw score to z score transformation, an associated value on the z table provides the percentage of scores:
between the mean and the z score
A hypothesis test is said to be ________ when it produces fairly accurate results, even when some of the assumptions underlying the hypothesis test are violated.
robust
