Intro to Statistics Exam 1
One purpose of a z-score is to standardize a score so that it can readily be compared with scores from other distributions that also have been transformed into z-scores. True or False
True
Which proportion of a normal distribution is located between z = 0 and z = +1.50? a) 0.4332 b) 0.9332 c) 0.4787 d) 0.0668
a) 0.4332
You determine the characteristics of the DSM to answer which of the following questions? a) Given a particular sample value, what is the probability of obtaining that value if the null hypothesis is true? b) Given a particular sample value, what is the probability of obtaining that value if the research hypothesis is true? c) Given a particular population value, what is the probability of obtaining that value if the null hypothesis is false? d) Given a particular population value, what is the probability of obtaining that value if the research hypothesis is true?
a) Given a particular sample value, what is the probability of obtaining that value if the null hypothesis is true?
All random samples of size n = 9 are selected from a normal population with µ = 55 and σ = 10, and the mean is computed for each sample. Then, all the possible samples of size n = 36 are selected from the same population, and the mean is computed for each sample. Which statement below is true. a) The distribution of sample means for samples of n = 36 is less variable than the distribution of sample means for n = 9. b) The distribution of sample means for n = 9 has a smaller mean than the distribution of sample means for n = 36. c) The distribution of sample means for n = 36 has a smaller mean than the distribution of sample means for n = 9. d) The distribution of sample means for samples of n = 9 is less variable than the distribution of sample means for n = 36.
a) The distribution of sample means for samples of n = 36 is less variable than the distribution of sample means for n = 9.
Percentiles are a type of statistic even though they do not summarize an entire distribution but rather is used to locate individual scores within a distribution of scores. a) descriptive b) population c) parameter d) inferential
a) descriptive
A Type I error is the result of: a) incorrectly rejecting the null hypothesis b) incorrectly accepting the null hypothesis c) improper measurement techniques on the part of the researcher d) failing to reject the null hypothesis when, in fact, it is true
a) incorrectly rejecting the null hypothesis
The actual values of the mean, variance, and standard deviation of a population are called: a) population parameters b) population Z scores c) sample statistics d) regressed standardized scores
a) population parameters
Decision errors are possible in hypothesis testing because you are making decisions about _______ based on information in ________. a) populations; samples b) samples; populations c) distributions; frequency tables d) distributions; Z tables
a) populations; samples
A hypothesis test involves a comparison of which two elements? a) research results from a sample and a hypothesis about a population b) research results from a sample and a hypothesis about the sample c) research results from a population and a hypothesis about a sample d) research results from a population and a hypothesis about the population
a) research results from a sample and a hypothesis about a population
What is measured by the denominator of the z-score test statistic? a) the amount of error expected between the sample mean and hypothesized population mean b) the position of the sample mean relative to the critical region c) the distance between the sample mean and hypothesized population mean d) the boundaries for the critical region(s)
a) the amount of error expected between the sample mean and hypothesized population mean
When making a frequency table for a nominal variable, the values listed on the left-hand side of the frequency table should be: a) the categories of the variable b) the percent correct c) the appropriate interval groupings d) the number of social interactions per week
a) the categories of the variable
What is measured by the numerator of the z-score test statistic? a) the distance between the sample mean and hypothesized population mean b) the boundaries for the critical region(s) c) the position of the sample mean relative to the critical region d) the likely distance between M and µ that would be expected if H0 was false
a) the distance between the sample mean and hypothesized population mean
The mean of a distribution of means is: a) the same as the original population mean b) the original population mean divided by the sample size c) the square root of the original population mean d) the sample mean multiplied by the variance
a) the same as the original population mean
Which combination of factors is more likely to produce small standard error? (No calculations are necessary). a) σ = 2; n = 9 b) σ = 10; n = 9 c) σ = 5, n = 9 d) Need more information to answer
a) σ = 2; n = 9
A researcher administers a new treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis? a) σ = 5 and α = .05 b) σ = 5 and α = .01 c) σ = 10 and α = .05 d) σ = 10 and α = .01
a) σ = 5 and α = .05
A random sample of n = 25 scores is selected from a normal population with µ = 90 and σ = 10. What is the probability that the sample mean will have a value less than 91? a) .9772 b) .6915 c) .3085 d) .0228
b) .6915
Which proportion of a normal distribution is located in the tail below z = -1.00? a) -0.1587 b) 0.1587 c) 0.8413 d) -0.3413
b) 0.1587
Which proportion of a normal distribution is located between z = 0 and z = +1.50? a) 0.0668 b) 0.4332 c) 0.9332 d) 0.4787
b) 0.4332
Suppose a normal distribution has a µ = 15 and a standard deviation σ = 5. Between what values of x do 68% of the values lie? a) 5 and 25 b) 10 and 20 c) 20 and 25 d) 15 and 25
b) 10 and 20
The mean score on a creativity test is 20 and the standard deviation is 5. The distribution is normal. Using the percentage approximations for the normal curve, how many people would attain a score between 15 and 25? a) 50% b) 34% + 34% = 68% c) 34% d) 14% + 34% = 48%
b) 34% + 34% = 68%
Which of the following is an example of a nominal variable? a) Number of friends a person has (0, 1, etc.) b) Nationality of the car a person owns (American, Japanese, etc.) c) Birth position in a family (first, second, etc.) d) Grade point average (3.2, 2.7, etc.)
b) Nationality of the car a person owns (American, Japanese, etc.)
A researcher tests whether a new teaching method is more effective than the old one. What is the alternative (research) hypothesis? a) There is some difference in effectiveness between the old teaching method and the new teaching method, but which is more effective is not predicted. b) The new teaching method is more effective than the old teaching method. c) The old teaching method is more effective than the new teaching method. d) There is no difference in effectiveness between the old teaching method and the new teaching method.
b) The new teaching method is more effective than the old teaching method.
What is the "cutoff" z value on the DSM? a) The point at which, assuming the research hypothesis is true, it would be extremely unlikely to get a result this extreme. b) The point at which, assuming the null hypothesis is true, it would be extremely unlikely to get a result this extreme. c) The point at which you accept the null hypothesis if the result is more extreme. d) The point at which the comparison distribution ends.
b) The point at which, assuming the null hypothesis is true, it would be extremely unlikely to get a result this extreme.
(Population 1M - Population 2M)/Population SD is a formula for figuring: a) the combined standard deviation b) effect size c) the variance of the distribution of means d) power
b) effect size
The advantage of a large sample size, like those used in polls, is that they: a) increase the score needed for a significant result b) greatly reduce the standard deviation of the distribution of means c)decrease the probability of correctly rejecting the null hypothesis d) increase the probability of a Type I error
b) greatly reduce the standard deviation of the distribution of means
In principle, you could make a distribution of means by: a) figuring the mean of all the possible samples of a given size and dividing it by the variance b) randomly taking a very large number of samples from a population, each of the same size, and making a distribution of their means c) using the sample's mean and variance divided by the population's parameters d) randomly estimating the population variance from the various samples of the same size, and using the sample mean in place of the population mean
b) randomly taking a very large number of samples from a population, each of the same size, and making a distribution of their means
Which is the expected value of M? a) the sample mean b) the mean of the distribution of sample means c) the population standard deviation d) the standard deviation of the distribution of sample means
b) the mean of the distribution of sample means
In general, the shape of a distribution of sample means (DSM) tends to be: a) bimodal, symmetrical b) unimodal, symmetrical c) unimodal, skewed d) rectangular, symmetrical
b) unimodal, symmetrical
When is a researcher at risk of making a Type I error? a) whenever H0 fails to be rejected b) whenever H0 is rejected c) whenever H1 is rejected d) The risk of a Type I error is independent of the decision from a hypothesis test.
b) whenever H0 is rejected
According to Cohen's effect size conventions for mean differences, the following represent small, medium, and large effects, respectively: a) .5, .8, 1.0 b) .2, .3, .5 c) .2, .5, .8 d) .4, .75, .90
c) .2, .5, .8
For a population, a sample of n = 36 scores has a standard error (σM) of 3. For the same population, a sample of n = 81 would have standard error of what? a) None of the options is correct. b) 18 c) 2 d) 3
c) 2
For a population, a sample of n = 25 scores has a standard error (σM) of 4. For the same population, a sample of n = 16 would have standard error of what? a) 4 b) 20 c) 5 d) 2
c) 5
How do you determine whether or not to reject the null hypothesis? a) If the Z score is greater than +2.5 b) Compare the standard deviation of the sample to the standard deviation of the population c) Compare the Z score needed to reject the null hypothesis to the actual sample Z score d) If the Z score is less than -1 or greater than +1
c) Compare the Z score needed to reject the null hypothesis to the actual sample Z score
The null hypothesis states: a) The population mean after treatment is not the same as it was before treatment b) The sample mean after treatment is the same as it was before treatment c) The population mean after treatment is the same as it was before treatment d) The sample mean after treatment is not the same as it was before treatment
c) The population mean after treatment is the same as it was before treatment
A __________ describes a particular score in terms of where it fits into the overall group of scores. a) Q score b) standard deviation c) Z score d) computational formula
c) Z score
Failing to reject the null hypothesis when the research hypothesis is true is referred to as: a) the error term b) the probability of rejection c) a Type II error d) a Type I error
c) a Type II error
A sample is selected from a normal population with a mean of µ = 40. If the sample mean is M = 45, which of the following combinations would make the sample mean a typical, representative value for the population? a) a small sample and a small population standard deviation b) a large sample and a large population standard deviation c) a small sample and a large population standard deviation d) a large sample and a small population standard deviation
c) a small sample and a large population standard deviation
When making a frequency table for a numeric variable, the list down the left edge of the page should include: a) only even-numbered values b) only odd-numbered values c) all possible values listed d) the cumulative frequencies and percentages for female participants
c) all possible values listed
When working with a nominal variable, the histogram is called a(n): a) bubble plot b) area plot c) bar graph d) frequency polygon
c) bar graph
The fact that probabilities are proportions means that they: a) can't be lower than zero or more than .05 b) have to be larger than one c) can't be lower than zero or more than one d) can be either a positive or a negative number
c) can't be lower than zero or more than one
The _____________ explains why many distributions tend to be close to normal in the real world. a) triples list calculation b) Pythagorean theorem c) central limit theorem d) normal curve table
c) central limit theorem
Practical significance is a combination of statistical significance and: a) the population parameters b) the amount over or under that level that the sample scored c) effect size d) the level of measurement (whether it is equal interval or ordinal)
c) effect size
The mean score on a political attitude scale is 5 and the standard deviation is 2. The distribution is normal. Using the percentage approximations for the normal curve, how many people would get a score between 5 and 9? a) 50% b) 34% + 34% = 68% c) 34% d) 34% + 14% = 48%
d) 34% + 14% = 48%
Suppose a normal distribution has a µ = 15 and a standard deviation σ = 5. Between what values of x do 95% of the values lie? a) 10 and 20 b) 15 and 35 c) 25 and 35 d) 5 and 25
d) 5 and 25
Which statement accurately describes the proportions in the body of a normal distribution? a) Body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50. b) Body proportions are always ≤ .50. c) Body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50. d) Body proportions are always ≥ .50.
d) Body proportions are always ≥ .50.
Which statement accurately describes the proportions in the body of a normal distribution? a) Body proportions on the right side of the z-score are less than 0.50; on the left side, they are greater than 0.50. b) Body proportions are always ≤ .50. c) Body proportions are always ≥ .50. d) Body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50.
d) Body proportions on the right side of the z-score are greater than 0.50; on the left side, they are less than 0.50.
Critical region can be described as: a) The difference between the sample mean and population mean b) Outcomes that are expected if the null is true c) Another way of saying alpha level d) Outcomes that are very unlikely if null is true
d) Outcomes that are very unlikely if null is true
If a researcher is interested in studying a phenomena but the characteristic is not normally distributed in the population, what suggestions would you give this professional to help her conduct her work? a) Quit now, it is not possible to continue with this research. b) Identify characteristics that are represented by a normal distribution. c) Use JASP to check for homogeneity of variance. d) Select a large sample (n > 30) and let the central limit theorem do the work.
d) Select a large sample (n > 30) and let the central limit theorem do the work.
What does it mean if a researcher said she rejected the null hypothesis at the .05 level? a) There is a 5% chance that there is a difference between the two populations she is testing if the null hypothesis were true. b) There is a 95% chance that the research hypothesis is true. c) There was more than a 5% chance that she would have gotten such an extreme result by chance if the null hypothesis were true. d) There was less than a 5% chance that she would have gotten such an extreme result by chance if the null hypothesis were true.
d) There was less than a 5% chance that she would have gotten such an extreme result by chance if the null hypothesis were true.
Delores must grade a driver's test completed by a group of training students. She knows that driver's test scores are normally distributed with µ = 50 and σ = 6. Students are required to score in the top 75% of students on the test in order to pass the test and continue on with the training course. Which score do students need to obtain at a minimum in order to pass the test and continue with the course? a) X = 60 b) X = 40 c) X = 54 d) X = 46
d) X = 46
As the number of individuals in each sample gets larger, the distribution of means: a) becomes more positively skewed b) becomes more negatively skewed c) begins to look less and less like the normal curve (in terms of shape) d) becomes a better approximation of the normal curve (in terms of shape)
d) becomes a better approximation of the normal curve (in terms of shape)
What statement below is consistent with making a Type II error? a) concluding that a treatment has no effect when it really has no effect b) concluding that a treatment has an effect when it really does c) concluding that a treatment has an effect when it really has no effect d) concluding that a treatment has no effect when it really does
d) concluding that a treatment has no effect when it really does
What is the probability of randomly selecting a z-score less than z = +2.25 from a normal distribution? a) p = 0.4878 b) p = 0.2112 c) p = 0.0122 d) p = 0.9878
d) p = 0.9878
