statistical methods in psychology #2
If a population is normally distributed, with μ=150 and σ=10, we know that approximately ____% of the scores fall between 140 and 160. Give the approximate answer, do not include the percent sign.
68
For all normal curves, ____% of the scores fall within 1 standard deviation of the mean (go to two decimal places, do not include the % sign).
68.26
In which of the following samples did the scores differ more from each other? Assume there is no outlier affecting the measures. Sample One: S=235 Sample Two: S=741
Sample Two: S=741
power + beta =
1
If H0 is true, what is the probability that your data will lead you to incorrectly decide to reject H0? In other words, the probability of making a Type 1 error when H0 is true is called....
alpha
Once you decide upon a significance level that also sets the value of ______.
alpha
The hypothesis you hope to prove, the one that proposes that real differences exist, that the data are not simply due to random sampling error, is called the _________ hypothesis.
alternative
That the average of the sample means equals the mean of the population from which the samples were drawn is why the sample mean is __ ______ _______ of the population mean.
an unbiased estimate
A normal curve is shaped like a _______.
bell
If H0 is false, what is the probability that your data will lead you to incorrectly decide to not reject H0? In other words, the probability of making a Type 2 error when H0 is false is called....
beta
If your decision is to 'reject H0', what does that imply about Ha?
accept Ha
When the occurrence of one event makes it neither more nor less probable that the other event will occur as well then the two events are said to be ____________ .
independent
Event A and Event ~A are:
mutually exclusive and exhaustive
The two hypotheses (H0 and Ha) are
mutually exclusive and exhaustive
To say that two events can't both happen is to say that they are
mutually exclusive events
We are sampling 15 scores from a population, can we reasonably count on the SDM being normally distributed?
no
'~A' represents.
not A
In null hypothesis testing you start by determining the probability of having obtained your data if the null hypothesis were true. If that probability is quite low then you decide to _________ the null hypothesis.
reject
Which of the following are the only two possible (official) results of an experiment?
reject H0 do not reject H0
When running an experiment what we actually have to base our decision upon are...
samples
The standard deviation of the SDM is also known as the
standard error
The score that reflects how many standard deviations above or below the mean a particular score falls is called the _________ __________ .
standard score
In the previous question: "You are going to sample from a population that is normally distributed with μ=65 and a σ=9, if you sample six scores from the population what is the probability that the sample mean will be at least 4 away from the population mean in either direction, in other words, p(M≤61 or M≥69)=?" What type of probability is that?
two-tail p value
We are sampling 40 scores from a population, can we reasonably count on the SDM being normally distributed?
yes
Which of the following is the symbol for the mean of the SDM?
μM
The general rule of thumb for how large N needs to be for us to count on the SDM being normally distributed is for N to be ≥ ____
30
What has to be true for the theoretical approach to work?
Every possible event has an equal chance of occurring
When expressed as a proportion probability will always be a value between ___ and ____.
0 and 1.00
When expressed as a percent probability will always be a value between ___% and ____%.
0, 100
Consequently in psychological experiments, the probability that you will reject H0 when the H0 is actually true =
0.05
In psychology the most commonly used value for the significance level is _____
0.05
You sample 15 scores from a population that is normally distributed with μ=230 and σ=50. State the value of the mean of the SDM. μM = ?
230
When you roll a six-sided die every face (1,2,3,4,5,6) has an equal chance of occurring. Define event A as rolling a '2' and event B as rolling a number that is below '4'. We found in the previous questions that p(A)=0.17 and p(A|B)=0.33, what if anything does that tell you about whether A and B are independent?
A and B are not independent
If in reality H0 is false and your data lead you to reject H0, what would that be?
A correct decision
If in reality H0 is true and your data lead you to not reject H0, what would that be?
A correct decision
If in reality H0 is true and your data lead you to reject H0, what would that be?
A type 1 error
If in reality H0 is false and your data lead you to not reject H0, what would that be?
A type 2 error
In some other scenario, p(C)=0.8, p(C|D)=0.8 , what if anything does that tell you about whether C and D are independent?
C and D are independent
The theorem that states the SDM will be normally distributed if N is large enough is called the
Central Limit Theorem
Which of the following will lead to more precise confidence intervals?
Drawing a large sample. Drawing from a population that has a small variance.
If event A is defined as the probability of drawing a black card from a normal deck of 52 cards, then p(~A) would be the probability of...
Drawing anything but a black card
Timmy comes home from school with grades from exams in the following subjects: Math Y=145, z=-1.89 English Y=32, z=2.5 Geography Y=10, z=0.2 In which class did he do very well compared to other students in the class?
English
Timmy comes home from school with grades from exams in the following subjects: Math Y=145, z=-1.89 English Y=32, z=2.5 Geography Y=10, z=0.2 In which class did he do about average compared to other students in the class?
Geography
Which of the following is the symbol for the null hypothesis?
H0
Which of the following is the symbol for the alternative hypothesis?
Ha
What effect does a large amount of variability in the population have on the probability of getting a nonrepresentative sample?
Makes is more likely
p(A|B) is read as...
The probability of event A given event B
Which would give you, on the average, more accuracy when using the sample mean to predict the population mean? When the standard error of the SDM (i.e. σM) = 18.5 When the standard error of the SDM (i.e. σM) = 5.3
When the standard error of the SDM (i.e. σM) = 5.3
When do we have to use the "t distribution" rather than a "normal distribution" to get the correct "p values"?
When we have to estimate the standard deviation of the population.
In which of the following two samples would the variance and standard deviation not do a very good job of describing the variability of the scores? Y = 3, 80, 80, 80, 80, 80 Y = 45, 48, 52, 53, 57
Y = 3, 80, 80, 80, 80, 80
One study of the heights of trees in a forest used inches as the measure of height, another study of the very same trees used feet as the measure of height. Would the two studies arrive at different values for the standard deviation?
Yes
Say that you are flipping a fair coin, one that has an equal chance of coming up heads or tails, and by some freakish chance you happen to get 20 heads in a row. What is the probability that the next flip will also be a head?
equal to .50 as the tosses of the coin are independent
To say that the definition of two events cover every possible event that could occur would be to say that the events are ______________.
exhaustive
The probability of event 'A' occurring is symbolized as _______
p(A)
Will we now move away from the data above and talk about confidence intervals in general. Which of the following confidence intervals provides a more precise idea of the plausible values of μ? 45 ≤ μ ≤ 68 55 ≤ μ ≤ 58
55 ≤ μ ≤ 58
If a population is normally distributed, with μ=150 and σ=10, we know that approximately ____% of the scores fall between 130 and 170. Give the approximate answer, do not include the percent sign.
95
For all normal curves, ____% of the scores fall within 2 standard deviations of the mean (go to two decimal places, do not include the % sign).
95.44
If a population is normally distributed, with μ=150 and σ=10, we know that over ____% of the scores fall between 120 and 180. Give the approximate answer, do not include the percent sign.
99
For all normal curves, ____% of the scores fall within 3 standard deviations of the mean (go to two decimal places, do not include the % sign).
99.74
You sample 15 scores from a population that is normally distributed with μ=230 and σ=50 and you write down the mean of that sample. You then repeat this an infinite number of times, each time sampling 15 scores from that population and noting the mean of the sample. What will be the average (mean) value of those sample means?
230
Y = 34, 23, 33, 29 df=?
3
Timmy comes home from school with grades from exams in the following subjects: Math Y=145, z=-1.89 English Y=32, z=2.5 Geography Y=10, z=0.2 In which class did he do very poorly compared to other students in the class?
Math
The abbreviation for the sampling distribution of the mean is the '____'.
SDM
In which of the following samples did the scores differ more from each other? Assume there is no outlier affecting the measures. Sample One: S=5.24 Sample Two: S=0.89
Sample One: S=5.24
In the empirical approach why do you have to sample with replacement?
So that you sample from the same population each time
What has to be true for the empirical approach to work?
That you sample with replacement
In null hypothesis testing you start by determining the probability of having obtained your data if the ________ hypothesis were true.
null
The hypothesis you hope to disprove, the one that usually proposes that no real difference exists, that any apparent patterns in your data are simply due to random sampling error, is called the ______ hypothesis.
null
In the previous question: "You are going to sample from a population that is normally distributed with μ=65 and a σ=9, if you sample six scores from the population what is the probability that the sample mean will be at least 4 below the population mean, in other words, p(M≤61)=?" What type of probability is that?
one-tail p value
Which of the following best describes the relationship between p(A|B) and p(B|A)?
p(A|B) doesn't necessarily equal p(B|A) for they are two different things.
The sampling distribution of the mean is itself a:
population
When running an experiment what we want to know about are...
populations
If H0 is false, what is the probability that your data will lead you to correctly decide to reject H0?
power
The distribution of all the sample means you could obtain if you sample a specific number of scores from a specific population is called the
sampling distribution of the mean
How improbable the results have to be to reject H0 is called your
significance level
If the null hypothesis proposes that two samples come from populations that have identical means, then which would be more probable?
that the two sample means will be similar in value
Which of the following is the symbol for the standard deviation of the SDM?
σM
We randomly sample five scores from a population that is normally distributed with a mean of 40 (i.e. 𝝁=40). Y= 38, 39, 42, 44, 46 M=41.8 Our sample mean was 1.8 above the population mean. We want to determine the probability that we would have obtained a sample mean that is 1.8 or more away from the population mean (in either direction). In other words p(M ≤ 38.20 or M ≥ 41.80). To do this we need to look at all of the sample means we might obtain (i.e. the SDM) if we sample five scores from that population. Is the standard deviation of the population given in this story problem?
No, so we will need to use the t distribution.
We are sampling 5 scores from a population that is normally distributed, can we reasonably count on the SDM being normally distributed?
yes
You sample 15 scores from a population that is normally distributed with μ=230 and σ=50. Can you count on the SDM being normally distributed?
yes
