psych stats exam 2 study guide
pn = ?
mean
a z-score of _______ is associated with a 1-tailed test and a = .05
+1.645
what are the mean and standard deviation of a distribution of z-scores?
0 and 1
method that uses sample data to statistically evaluate an educated guess about a population
hypothesis test
A population with μ = 85 and σ = 12 is transformed into z-scores. After the transformation, the population of z-scores will have a standard deviation of σ = ___ ?
1.00
If a multiple choice quiz has 100 questions in which every question has 4 choices, what is the probability of getting fewer than 20 questions correct merely by guessing?
10%
A vertical line is drawn through a normal distribution at z = -1.00. How much of the distribution is located between the line and the mean?
34.13%
A random sample is selected from a normal population with a mean of μ = 200 and a standard deviation of σ = 12. After a treatment is administered to the individuals in the sample, the sample mean is found to be M = 196. How large a sample is necessary for this sample mean to be statistically significant using a two-tailed test with α = .05?
35
for a population with a µ = 40 and σ = 11, find the z-score for each of the following X values. x= 45 x= 30 x= 52 x= 25 x= 41 x= 38
45: z= .45 30: z= -.91 52: z= 1.09 25: z= -1.36 41: z= .09 38: z= -.18
a population of scores has σ = 4. In this population, an X value of 58 corresponds to z = 2.00. What is the population mean?
50
If all the possible random samples of size n = 7 are selected from a population with μ = 70 and σ = 5 and the mean is computed for each sample, then what value will be obtained for the mean of all the sample means?
70
When Lorenzo finished his exam last week, he thought the test was over. But the instructor put z-scores on each student's paper and asked them to figure out their original score. The mean for the class is µ = 61 and standard deviation is σ = 8. Lorenzo's z-score is +1.75. What did he score on the exam?
75
a population of scores has μ = 44. In this population, an X value of 40 corresponds to z = -0.50. What is the population standard deviation?
8
For a normal distribution with μ = 100 and o = 10, what X values separate the middle 95% from the extreme values in the tails of the distribution? (2 values)
80.4 and 119.6
A population of plant heights has a mean of μ = 13 and standard deviation of σ = 2. What is the probability of an individual plant having a height between 10 and 16?
86.64%
Which of the following are correct ways of defining the power of a statistical test? I. The probability that the test will correctly reject a false null hypothesis II. The probability that the test will result in a Type II error III. The probability that the test will not result in a Type II error
I and III
If you are simply guessing on a true/false test with 36 questions, what is the probability that you will get 20 or more correct?
0.3085
A population has μ = 50 and σ = 10. If these scores are transformed into z-scores, the population of z-scores will have a mean of ____ and a standard deviation of _____
0; 1
If a sample with M = 60 and s = 8 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of _______ and a standard deviation of ________
0; 1
theorem states there is a change, a difference, or a relationship for the general population
alternative hypothesis
population in which each individual has an equal, non-dependent chance of being selected
independent random sample
A treatment is administered to a sample selected from a population with a mean of μ = 40 and a standard deviation of σ = 6.25. After treatment, the sample mean is M = 45. Based on this information, the effect size as measured by Cohen's d can be classified as what?
large effect
𝘔 is an example of a ______________
sample statistic
discrepancy that naturally occurs between a selection statistic and its corresponding population parameter
sampling error
d = 0.2 has a _________ effect (mean difference around 0.2 standard deviation)
small
standard deviation of the distribution of sample means
standard error of M
x - pn / square root of npq = ?
z-score
A researcher has compiled a set of scores with a mean of µ = 39 and standard deviation of σ = 4. What is the z-score for the raw score X = 28?
z= -2.75
A sample has a mean of M = 64 and standard deviation of s = 3. What is the z-score for a sample score of X = 70?
z=+2.00
What is necessary to determine the z-score for a raw score in a particular set of scores?
the mean and standard deviation for the set
what information is provided by the sign (+/-) of a z-score?
whether the score is located above or below the mean
A distribution with µ = 61 and σ = 6 has been standardized to reflect a new mean of µ = 50 and a standard deviation of σ = 10. What is the new standardized score for a score of X = 52 in the original distribution?
x=35
for a population with μ = 100 and σ = 20, what is the z-score corresponding to X = 105?
+0.25
A random sample of n = 9 scores is obtained from a population with μ = 50 and o = 9. If the sample mean is M = 53, what is the z-score corresponding to the sample mean?
+1.00
A distribution with μ = 47 and σ = 6 is being standardized so that the new mean and standard deviation will be μ = 100 and σ = 20. What is the standardized score for a person with X = 56 in the original distribution?
130
What happens to the standard distance between the sample mean and the population mean when the sample size is multiplied by 4?
it is divided by 2
The standard error for a particular sample is 3.6. A researcher needs the standard error to be 1.2. What should the researcher do to the sample size?
multiply the sample size by 9
A random sample is normally distributed. If all values in the sample and all values in the population are multiplied by 2, what is the impact on Cohen's d?
stays the same
What is the benefit of converting raw scores from a sample into z-scores?
the new scores are easier to compare
p = p(A) = ________________
the probability of A
q = p(B) = __________________
the probability of B
When computing z for a sample mean, which quantity is used?
the standard error
When a researcher rejects a null hypothesis that is actually true
type I error
chart listing proportions corresponding to each z-score location in a normal distribution
unit normal table
probability of a Type II error
beta
A random sample of n = 25 scores is selected from a normally distributed population with μ = 500 and o = 100. What is the probability that the sample mean will be less than 490?
0.3085
For a normal population the sample mean M = 35 has the same z-score as the sample mean M = 43. What is the population mean?
39
A distribution with μ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be μ = 50 and σ = 10. In the new, standardized distribution your score is X = 60. What was your score in the original distribution?
43
What is the correct decision in a hypothesis if the data produce a z-score that is in the critical region?
Reject the null hypothesis
what is the type I error symbol?
a
A normal population has μ = 50 and o = 8. A random sample of n = 16 scores from this population has a mean of 54. What is the z-score for this sample mean?
+2.00
what z-score separates the lowest 10% of the distribution from the rest? z = _________ ?
-1.28
For a sample with a standard deviation of s = 5, what is the z-score corresponding to a score that is located 10 points below the mean?
-2
What is the z-score for a sample mean of M = 21 where the population mean is 24, the population standard deviation is 3, and the sample size is 16?
-4
A beetle population has a mean length of 2.3 inches with standard deviation of 0.2 inches. What is the standard error for a sample size of 16?
.05
There are 12 blue marbles, 8 red marbles, and 20 green marbles in a jar. A marbles is drawn from the jar and replaced. This is repeated 4 times, and each time a green marble is drawn. On the fifth time, what is the probability of drawing a green marble?
.5
for a binomial distribution with p = 1/4, what is the probability that A will occur more than 18 times in a series of 48 trials?
0.0150
for a normal distribution with a mean of μ = 40 and o = 4, what is the probability of selecting an individual with a score greater than 46 ?
0.0668
what proportion of a normal distribution is located in the tail beyond a z-score of z= -1.50?
0.0668
A population of birth weights has a mean of μ = 8.1, and a standard deviation of σ = 0.1. What is the probability of an individual weight being greater than 8.4?
0.13%
for a normal distribution with a mean of μ = 500 and o = 100, what is the probability of selecting an individual with a score less than 400?
0.1587
A population has a mean of 120 and a standard deviation of 10. If a sample of size 25 is collected, how much distance on average is expected between the sample mean and the population mean?
2
A jar contains 20 red marbles and 10 blue marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both red, what is the probability that the third marble also will be red?
20/30
The number of minutes spent reading in one day is normally distributed with a mean of μ = 23 and a standard deviation of σ = 5. How much time would you have to spend reading in a day to find yourself in the top 10% of readers?
29.4
If random samples, each with n = 4 scores are selected from a population with μ = 80 and o = 12, then how much distance is expected on average between the sample means and the population mean?
6 points (12/square root (4))
SAT scores for a normal distribution with a mean of μ = 500 with a o = 100. What SAT score separates the top 10% of the distribution from the rest?
628
a population of scores has σ = 10. In this population, a score of X = 60 corresponds to z = -1.50. what is the population mean?
75
For a sample with a standard deviation of s=8, a score of x=65 corresponds to z = 1.50. What is the sample mean?
M=53
A study is conducted to see if teenagers drive at faster average speeds than the general population of drivers. The average speed of the driving population is 35 mph. The null hypothesis is H0: μaverage driving speed of teenagers = 35 mph. What is the alternative hypothesis? a. H1: μdriving speed of teenagers = 35 mph b. H1: μdriving speed of teenagers ≠ 35 mph c. H1: μdriving speed of teenagers > 35 mph d. H1: μdriving speed of teenagers < 35 mph
b
hypothesis that specifies the characteristics of the distribution of sample means
central limit theorem
measure of effect size computed by dividing the mean difference by the standard deviation
cohen's d
what is step 3 of hypothesis testing?
compute the test statistic (the z-score)
Which of the following is not a valid probability? a. 0 b. 75% c. 1 d. 6/5
d
Professor Chao's engineering final exam has a mean of µ = 79 and σ = 7. After standardizing the exam scores, the mean is µ = 80 and σ = 5. How did Professor Chao arrive at these new standardized scores for the exam?
deciding what values will be simple to calculate
the standard error of 𝘔 __________ as sample size increases
decreases
measures the distance in points between X and μ and indicates whether X is located above or below the mean
deviation score
the distance, and direction, from the mean to a specific score
deviation score
measurement of the absolute magnitude of a treatment's influence on the dependent variable
effect size
what is step 2 of hypothesis testing?
locating critical region
Marisol received a score of X = 70 on her chemistry exam and a score of X = 59 on her geography exam. The mean for the chemistry exam is µ = 66, and the mean for the geography exam is µ = 50. On which exam will Marisol receive a higher grade?
unknown (the standard deviation for each set of exam scores is required)
numerical value equal to the distance from the mean measured in standard deviations
z-score
A calculus exam has a mean of µ = 73 and a standard deviation of σ = 4. Trina's score on the exam was 79, giving her a z-score of +1.50. The teacher standardized the exam distribution to a new mean of µ = 70 and standard deviation of σ = 5. What is Trina's z-score for the standardized distribution of the calculus exam?
z=+1.50
A distribution of scores for a test of life stressors has a mean of µ = 125 and standard deviation of σ = 15. The researcher calculates z-scores to standardize the distribution. What are the mean (µ) and the standard deviation (σ) for the z-scores in this distribution?
µ = 0, σ = 1
In a sample distribution, X=56 corresponds to z=1.00, and X=47 corresponds to z= -.50. Find the mean and standard deviation for the sample. µ = σ =
µ = 50 σ = 6
Within a population having standard deviation of σ = 20, the raw score X = 75 has a z-score of -1.25. What is the mean (µ) for this population?
µ=100
a score that is 9 points above the mean corresponds to a z-score of z = 1.50. what is the population standard deviation (σ)?
σ = 6
A distribution has a standard deviation of σ = 20. Describe the location of each of the following z-scores in position relative to the mean. For example, z = +1.00 is a location that is 20 points above the mean. - z = +2.00 is located _____ the mean by ____ - z = +.50 is located ____ the mean by _____ - z = -1.00 is located _____ the mean by _____ - z = -.25 is located ____ the mean by _____
-above the mean by 40 points -above the mean by 10 points -below the mean by 20 points -below the mean by 5 points
For a sample with M = 60 and s = 8, what is the z-score corresponding to X = 62?
0.25
For a normal distribution with μ = 2 and σ = 0.5, what is p(X < 1.7) + p(X < 2.3)?
1
A researcher is evaluating the influence of a treatment using a sample selected from a normally distributed population with a mean of μ = 30 and a standard deviation of σ = 3. The researcher expects a 1-point treatment effect and plans to use a two-tailed hypothesis test with α = 0.05. Compute the power of the test if the researcher uses n = 9 individuals.
17%
a colony of laboratory rats contains 18 white rats and 7 spotted rats. What is the probability of randomly selecting a white rat from this colony?
18/25
A population of insect weights is normal with a mean of μ = 16. If the probability of a weight falling between 10 and 22 is 95.44%, what is the standard deviation for this distribution?
3
what is the standard deviation for a binomial distribution with p = q = 1/2 and n = 36?
3
for a population with a µ = 60 and σ = 12, find the z-score for each of the following X values. x=69, x=54, x=84, x=48, x=63, x=45 for the same population, find the score (x value) that corresponds to each of the following z-scores. .50, -.25, 1.5, -.50, -2.5, 1.25
69: z= .75 54: z= -.50 84: z= 2.00 48: z=-1.00 63: z= .25 45: z=-1.25 .50: x=66 -.25: x= 57 1.5: x=78 -.5: x=54 -2.5: x=30 1.25: x=75
All of the possible random samples of size 5 are selected from a population and the variance among these sample means is 16. If all possible random samples of size 10 are selected from the same population, what can we say about the variance of this new set of sample means?
It will be less than 16.
A distribution with a mean of µ = 76 and a standard deviation of σ = 12 is being transformed into a standardized distribution with a µ = 100 and σ = 20. Find the new, standardized score for each of the following values from the original population. X = 61, X=70, X=85, X= 94
X=75, X=90, X=115, X=130
A researcher administers a treatment to a sample of n = 100 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.1. Assuming that the researcher is using a two-tailed test, what should the researcher do? a. The researcher should reject the null hypothesis with α = .05, but not with α = .01. b. The researcher should reject the null hypothesis with either α = .05 or α = .01. c. The researcher should fail to reject the null hypothesis with either α = .05 or α = .01. d. Cannot answer without additional information.
a
Which of the following correctly describes the effect that decreasing sample size and decreasing the standard deviation have on the power of a hypothesis test? a. A decrease in sample size will decrease the power, but a decrease in standard deviation will increase the power. b. Both will increase the power. c. A decrease in sample size will increase the power, but a decrease in standard deviation will decrease the power d. Both will decrease the power
a
identify the exam score that should lead to the better grade: a. a score of X = 60 on an exam with µ = 72 and σ = 12. b. a score of X = 70 on an exam with µ = 82 and σ = 8 c. neither of these two scores
a
When is the distribution of sample means identical to the population distribution? a. When n = 1 b. When the standard error equals the population standard deviation c. When n is a very large number d. Both a and b
a and b
which of the following is equal to p(z > 2.00) in a normal distribution? a. p(z < -2.00) b. 1 - p(z < 2.00) c. ½ p(z > 1.00)
a and b
Which of the following is a true statement for any population with mean μ and standard deviation σ? I. The distribution of sample means for sample size n will have a mean of μ. II. The distribution of sample means for sample size n will have a standard deviation of σ/square root of n. III. The distribution of sample means will approach a normal distribution as n approaches infinity.
all of the above
Assuming a normal distribution, which of the following would call for a one-tailed hypothesis test rather than a two-tailed test? a. Determining if attending Harvard influences IQ b. Determining if driving a red car increases the number of speeding tickets per year c. Determining if being male influences height d. Determining if being a teenager influences the number of hours of sleep per night
b
If other factors are held constant, then how does the sample size affect the likelihood of rejecting the null hypothesis and the value for Cohen's d? a. A larger sample size increases the likelihood of rejecting the null hypothesis and increases the value of Cohen's d. b. A larger sample size increases the likelihood of rejecting the null hypothesis but does not change the value of Cohen's d. c. A larger standard deviation decreases the likelihood of rejecting the null hypothesis but increases the value of Cohen's d. d. A larger standard deviation decreases the likelihood of rejecting the null hypothesis and does not change the value of Cohen's d.
b
scale that shows the probability associated with each value of X
binomial distribution
For a binomial distribution with p = 0.75 and n = 15, the probability of A occurring more than 10 times is about 68.65%. Using a normal distribution with μ = 11.25, σ = 1.667, and p(X >10.5) to approximate this probability gives 67.26%. Which of the following best explains the discrepancy between the actual value of 68.65% and the approximation of 67.26%? a. p(X > 10) should have been used instead of p(X > 10.5). b. p(X > 9.5) should have been used instead of p(X > 10.5). c. np is not high enough to achieve a closer approximation. d. nq is not high enough to achieve a closer approximation
d
What would be the result of setting an alpha level extremely small? a. There would be almost no risk of a Type I error. b. It would be very difficult to reject the null hypothesis. c. Neither a nor b d. Both a and b
d
Which of the following is a common limitation of hypothesis testing? a. Conclusions are made about the data set rather than about the hypothesis itself. b. Demonstrating a significant treatment effect does not necessarily indicate a substantial treatment effect. c. Hypothesis testing loses its effectiveness for small samples. d. Both a and b
d
Which z-score mark separates the bottom 97.5% from the top 2.5% in a normal distribution? a. -1.96 b. -1 c. 1 d. 1.96
d
changing from a one-tailed to a two-tailed test ____________ the power of a hypothesis test
decreases
examination in which a particular vector of effect is statistically specified
directional test
collection of sample means for all the possible random samples of a particular size
distribution of sample means
mean of the distribution of sample means
expected value of M
what information is provided by the magnitude (numerical value) of the z-score?
how many standard deviations the score is away from the mean
identify the four steps in order of a hypothesis test: 1. state the ________ and select an _______ level 2. locate the ________ region 3. compute the _______ _________ 4. make a __________
hypotheses; alpha critical test statistic decision
If a researcher is concerned that a standard error is too big for the sample mean to provide a reliable measure of the population mean, what can the researcher do?
increase the sample size
increasing the alpha from .01 to .05 ____________ the power of a hypothesis test
increases
rule states that bigger sample sizes yield better approximations of population values
law of large numbers
what is step 4 of hypothesis testing?
make a decision about the null hypothesis
d = 0.5 has a ___________ effect (mean difference around 0.5 standard deviation)
medium
For samples selected from a population with μ = 90 and σ = 30, what sample size is necessary to make the standard distance between the sample mean and the population mean equal to 5 points?
n = 36
theorem states that in the general population there's no change, no difference, or no relationship
null hypothesis
probability that the test will correctly reject a false null hypothesis
power
population in which each individual has an equal chance of being selected
random sample
an original, untransformed observation or measurement
raw score
technique returns the current selection to the population before the next selection is made
sampling with replacement
Which of the following is not an assumption for hypothesis tests with z-scores?
small standard deviations
the square root of npq = ?
standard deviation
an entire distribution that has been transformed to create predetermined values
standardized distribution
what is step 1 of hypothesis testing?
state the null hypothesis and select an alpha level
In a distribution, a score of X = 60 has a z-score of -3.0. A score of X = 85 has a z-score of +2.0. What are the mean (µ) and the standard deviation (σ) for this population?
µ=75 σ=5
A researcher selects a sample of n = 20 from a normal population with μ = 80 and o = 20, and a treatment is administered to the sample. If a hypothesis test is used to evaluate the effect of the treatment, what is the null hypothesis?
μ = 80
A test of life satisfaction has a mean of µ = 60. Jenna's test score of X = 72 has a z-score of +3.0. What is the standard deviation (σ) for this distribution of test scores?
σ= 4
A distribution of 1000 test scores has a mean of µ = 287. Following standardization, what is the standard deviation for this distribution?
σ=1
A researcher is working with a population of data. He needs the standard distance between sample mean and the population mean to be at most 1.3. If the standard deviation of the population is 5, how large will the sample size need to be?
15
The population distribution of scores on a test is normal with μ = 40 and σ = 2. What is the probability of scoring less than a 38 on this test?
15.87%
For a distribution of exam scores with μ = 70, which value for the standard deviation would give the highest grade to a score of X =75? a. σ =1 b. σ = 2 c. σ = 5 d. σ = 10
A
if your exam score is X = 60, which set of parameters would give you the best grade? a. μ = 65 and σ = 5 b. μ = 65 and σ = 2 c. μ = 70 and σ = 5 d. μ = 70 and σ = 2
A
If a sample is selected from a normal population with μ = 50 and o = 20, which of the following samples is extreme and very unlikely to be obtained? a. M = 45, n = 4 scores b. M = 45, n = 25 c. M = 45, n = 100 d. all equally likely to be obtained
C
value with a common form across a distribution
standardized score
What is the probability of a z-score falling within one standard deviation of the mean in a normal distribution?
68.26%
Given that p = 0.5, for which value of n will the bar graph for the corresponding binomial distribution look most like a normal distribution? a. n=2 b. n=10 c. n=20 d. n=100
d
A distribution has µ = 50 and σ = 6. In a graphical representation of the distribution, where would the score X = 20 appear?
in the left tail of the curve
What is the probability of a z-score being less than 2 standard deviations from the mean in a normal distribution? a. 95% b. More than 95% c. Less than 95% d. It depends on the mean.
b
The population of scores on a nationally standardized test forms a normal distribution with μ = 300 and σ = 50. If you take a random sample of n = 25 students, what is the probability that the sample mean will be less than M = 280?
2.28%
changing raw scores into z-scores is known as a:
z-score transformation
process changes raw scores into standard scores with mean 0 and standard deviation 1
z-score transformation
A distribution of exam scores has a mean of µ = 52 and standard deviation of σ = 6. What is the z-score for the exam score X = 61?
z= +1.5
What is the primary concern when selecting an alpha value?
To minimize Type I errors
for each of the following populations, would a score of X = 85 be considered a central score or an extreme score? a. µ = 75 and σ = 15: b. µ = 80 and σ = 2: c. µ = 90 and σ = 20: d. µ = 93 and σ = 3:
a. central b. extreme c. central d. extreme
original, unchanged scores that are direct result of measurement
raw score
The natural error that exists between a sample and its corresponding population
sampling error
A researcher expects a treatment to produce a decrease in the population mean. The treatment is evaluated using a one-tailed hypothesis test. Which z-scores would lead us to reject the null hypothesis with α = .05? I. z = -1.75 II. z = 1.75 III. z = -1.6 IV. z = 1.6
I
Which of the following is not a step in a hypothesis test? a. State the null hypothesis about a population. b. Set the alpha level. c. If the sample data is not located in the critical region, we accept the null hypothesis. d. If the sample data is located in the critical region, we reject the null hypothesis.
c
Which of the following z-scores indicates an X value that falls farthest below the mean for the distribution? a. z = -.50 b. z = +2.00 c. z = -1.50 d. z = +1.25
c
For a normal distribution with a mean of 60 and a standard deviation of 5, what X values separate the middle 95% from the extreme values? a. X = 50.2 and X = 69.8 b. X = -1.96 and X = 1.96 c. X = 50 and X = 70 d. X = 55 and X = 65
a
what requirements must be satisfied to have a random sample? a. the sample is drawn without replacement b. the proportions of all subgroups in the sample are equal to their proportions in the population c. each individual has an equal chance of being selected d. if more than one individual is selected, the probabilities stay constant for each individual selected
c and d
As part of a clinical research project, a sample population has been using an experimental drug intended to improve memory. Study participants completed a comprehensive memory test following six weeks of treatment. The results were standardized and compared to mean results for the full population. Which of the following participants indicates promising results for this drug treatment? a. Liming, a 34-year-old woman with a memory test z-score of +1.25 b. Javier, a 48-year-old man with a memory test z-score of -.25 c. Ahmad, a 61-year-old man with a memory test z-score of +.50 d. Ellie, a 52-year-old woman with a memory test z-score of +2.75
d
For a population with µ = 69 and σ = 4, which of the following X scores will convert to a positive z-score of magnitude greater than 1.0? a. X = 65 b. X = 72 c. X = 62 d. X = 74
d
A random sample is obtained from a population with μ = 120 and σ = 20, and a treatment is administered to the sample. Which of the following outcomes would be considered noticeably different from a typical sample that did not receive the treatment?
n = 144 with M = 124
Which quantity decreases as the sample size increases?
standard error
allocation composed of scores that have been transformed into predetermined values for μ and σ
standardized distribution
identify the exam score that should lead to the better grade: a. a score of X = 32 on an exam with µ = 24 and σ = 4. b. a score of X = 26 on an exam with µ = 20 and σ = 2 c. neither of these two scores
b
If the standard error among sample means is small, which of the following is true? I. All the possible sample means are clustered close together. II. A researcher can be confident that any individual sample mean will provide a reliable measure of the population. III. A researcher must be concerned that a different sample could produce a different conclusion.
I and II
In a normal sample distribution with n = 16, the null hypothesis is rejected. If the sample size is changed to 64 with all other factors staying the same, what happens to the z-score and the decision about the null hypothesis? a. The z-score is doubled, and the null hypothesis is still rejected. b. The z-score is multiplied by 6, and the null hypothesis is still rejected. c. The z-score is doubled, and we fail to reject the null hypothesis. d. The z-score is multiplied by 6, and we fail to reject the null hypothesis.
a
The distribution for scores on a history exam has µ = 70 and σ = 4. The distribution for a set of scores on a sociology exam has µ = 68 and σ = 4. Tenisha scored 76 on both exams. Which of the following statements best describes the grades Tenisha will receive on her exams? a. She will receive a higher grade on the sociology exam based on standardization. b. She will receive the same grades on both exams because her raw scores are the same. c. She will receive a higher grade on the history exam based on standardization. d. She will receive the same grades on both exams because σ is the same for both distributions.
a
The wingspan of a population of insects is normally distributed with μ = 42 and σ = 4. Which of the following is true? a. It is possible for an insect in this population to have a wingspan of 30. b. It is likely for an insect in this population to have a wingspan of 30. c. It is unlikely an insect in this population to have a wingspan of 30.
a and c
A research report summarizes the results of the hypothesis test by stating, "z = 3.11, p < .01." Which of the following is a correct interpretation of this report? a. The null hypothesis was not rejected, and the probability of a Type I error is less than .01. b. The null hypothesis was not rejected, and the probability of a Type II error is less than .01. c. The null hypothesis was rejected, and the probability of a Type I error is less than .01. d. The null hypothesis was rejected, and the probability of a Type II error is less than .01.
c
Which of the following explains why it is easier to reject the null hypothesis with a one-tailed test than with a two-tailed test with all the same parameters? a. Because the standard deviation in a one-tailed test is larger than that for a two-tailed test b. Because z-scores are calculated differently in a one-tailed test c. Because the critical region is all on one side in a one-tailed test and needs to be split between the two tails in a two-tailed test d. Because a two-tailed test uses a bimodal distribution
c
Which of the following is not a characteristic of the distribution of sample means? a. The sample means should pile up around the population mean. b. The pile of sample means should tend to form a normal-shaped distribution. c. The sample means should have similar standard deviations as the population standard deviation. d. The larger the sample size, the closer the sample means should be to the population mean.
c
identify the exam score that should lead to the better grade: a. a score of X = 58 on an exam with µ = 49 and σ = 6. b. a score of X = 85 on an exam with µ = 70 and σ = 10 c. neither of these two scores
c
a score that has been transformed into a standard form
standardized score
What is the best explanation for why a normal distribution is only an approximation for a binomial distribution? a. Binomial values are discrete, and normal values are continuous. b. The means for the two distributions are different. c. The standard deviations for the two distributions are different. d. There are more outcomes in a normal distribution than in a binomial distribution.
a
