Psych Homework Question 2
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
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?
55 ≤ μ ≤ 58
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
-Estimate the standard deviation of the following curve.
7
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 3 standard deviations of the mean (go to two decimal places, do not include the % sign).
99.74
If in reality H0 is false and your data lead you to reject H0, what would that be? A type 2 errort
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
The t test has its most serious problems when
Both assumptions are violated in the same data
Where are we going to get the value for the standard error?
By estimating it from our data
In experiment one, t(6)=2.04, p=.0874 In experiment five (which had much less variance among the scores within each group), t(6)=5.20, p=.0020 Which experiment had more power (assuming the IV really did have an effect)?
Experiment Five (less variance)
In experiment one (which had 8 scores), t(6)=2.04, p=.0874 In experiment four (which had 16 scores), t(14)=3.11, p=.0077 Which experiment had more power (assuming the IV really did have an effect)?
Experiment Four (N=16)
Which of the following is the correct null hypothesis for this two-tailed test? In the following options 'a' stands for 'auditory' and 'v' for 'visual'.
H0: μa=μv
The researcher is testing a theory which predicts that reaction times should be faster (i.e. smaller) to auditory stimuli than to visual stimuli. Which of the following is the correct Null hypothesis for this one-tailed test?
H0: μa≥μv
Which of the following is the symbol for the null hypothesis?
HO
Which of the following is the symbol for the alternative hypothesis?
Ha
The researcher is testing a theory which predicts that reaction times should be faster (i.e. smaller) to auditory stimuli than to visual stimuli. Which of the following is the correct ALTERNATIVE hypothesis for this one-tailed test? In the following options 'a' stands for 'auditory' and 'v' for 'visual'.
Ha: μa<μv
Which of the following is the correct alternative hypothesis for this two-tailed test?
Ha: μa≠μv
If the populations are not normally distributed and the population variances are not equal then... Correct!
Neither the standard t test nor Welch's will work well
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.
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....t
beta
t(6)=2.04, p=.0874 If there are no serious confounding variables, then we can..
cannot determine whether or not the additive gas led to different gas mileage than the non additive gas
he theorem that states the SDM will be normally distributed if N is large enough is called the
central limit theorem
A variable (something other than random error and the independent variable) that could account for why the group means differ is called a _________ variable.
confounding
If that were the case, then age would be a _________ variable in this experiment.
confounding
An experiment explores whether reaction times differ to an auditory stimulus (a tone) compared to a visual stimulus (flash of light). What is the independent variable?
Type of stimulus (auditory or visual)
If the assumption that the populations have the same variance is violated then the best approach is to...
Use Welch's version of the t test
In an experiment, which of the following would be a justification for making the test one-tailed (that μ1 < μ2).
You are testing a theory which specifically predicts that M1 should be less than M2 Some previous, similar, experiment found that M1 < M2
'Power' is the probability that...
You will be able to Reject H0 when H0 is actually false
Another way of saying that is that 'power' is the probability that..
You will be able to conclude your independent variable had an effect when it actually did
In the example on skiing, in which type of design(s) would you have to be concerned that older people may prefer one type of skiing over the other. (select all that apply).
correational design quasi-experimental design
If your decision is to 'reject H0', what does that imply about Ha?t
accept Ha
Which of the following statements is (are) correct?
alpha is the probability that if H0 is true that we will incorrectly decide to reject H0
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....t
alphat
Once you decide upon a significance level that also sets the value of ______.
alphta
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
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Y= 38, 39, 42, 44, 46 𝝁=40 M=41.8 We want to know p(M ≤ 38.20 or M ≥ 41.80) so now compute the t value for M=38.20. t=? [Mark M=38.20 on your curve, and also write its t value. Shade the area to the left of that.]
-1.2
-In a population that is normally distributed with a mean of 66 and a standard deviation of 5, what proportion of the scores will be at least 7 away from the mean in either direction (i.e. Y<= 59 or Y>=73)?
0.1615
You sample with replacement from a card deck of unknown composition (i.e. this is not a normal deck of cards). In 30 samples you obtained five queen of hearts. What is the probability of drawing a queen of hearts?
0.17 (5/30)
Go to the t tool in Oak Software. Enter your df. You want to find a p value from your t value so select "t to p". We want the two-tailed p value (this is obvious if you drew the curve as we went along) so select the correct image. Enter either value of t, and then click on "Calculate". According to the t tool, the probability of obtaining a sample mean that is 1.8 or more away from the population mean (in either direction), is p=?
0.2964 (
-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'. p(A|B)=
0.33 (1/3)
-You are going to sample from a population that is normally distributed with μ=65 and σ=9, if you sample one score from the population, what is the probability that it will be at least 4 below the population mean, in other words, p(Y≤61)=? (It would be an excellent idea to draw a curve while working this out.)
0.33 (z= (61-65)/9=-0.44)
In a population that is normally distributed, what proportion of the scores will fall 0.40 or more standard deviations below the mean (i.e. z ≤ -0.40).
0.3446
If you are sampling from a population where 40% of the people own bicycles then the probability of any one person you randomly select owns a bicycle would be _____? State the probability as a proportion.
0.4
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'. p(B)=
0.5 (3/6)
If event A is defined as drawing a red marble from a bag of marbles, and p(A)=0.35, then p(~A)=?
0.65
-In a population that is normally distributed with a mean of 66 and a standard deviation of 5, what proportion of the scores will fall within ±7 of the mean (i.e. 59 ≤ Y ≤ 73)?
0.8385
M1=50 and M2=61 and the two-tailed p value is p=.09 For a one-tailed test of a theory which predicts that μ1 should be greater than μ2 , what would be the one-tailed p value? p=? (don't round)
0.955
-We sample 8 scores from a population that is normally distributed with a mean of μ=350 and a standard deviation of σ=20. What proportion of the sample means will fall within 17 of the population mean (i.e. 333 ≤ M ≤ 367)? Recommendation: draw the SDM and shade in the regions. Answer to four decimal places.
0.9836
-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'. p(B|A)=
1
power + beta =
1
Y= 38, 39, 42, 44, 46 𝝁=40 M=41.8 Our sample mean was 1.8 above the population mean, we want to know the probability of obtaining a sample mean that is 1.8 or more away from the population mean (in either direction), i.e. p(M ≤ 38.20 or M ≥ 41.80). Compute the t value for 41.80. t=? [Mark M=41.8 on your curve, and also write its t value. Shade the area to the right of that.]
1.2
You have a population with μ=40 and a variance (note this is a variance not a standard deviation) of σ²=16. Compute the standard score for a score of Y=45 compared to other scores in the population.
1.25
Estimate the standard error (the standard deviation of the possible sample means). est.σM=? [draw it on the SDM]
1.4966
What value of z gives a one-tail p value of .05 on the upper tail? z = ?
1.65
What values of z give a two-tail p value of .05 (.025 on each tail). z = ± ___? (Input the positive value)
1.96
As the standard deviation of the population from which we sampled is not known, we will need to estimate it. The sample is repeated again below, along with the SS of the sample. Begin by estimating the variance of the population from which we sampled. Y= 38, 39, 42, 44, 46 M=41.8 SS=44.80 est. σ2=?
11.2
-You sample 15 scores from a population that is normally distributed with μ=230 and σ=50. State the value of the standard error of the SDM. σM = ?
12.91
You repeatedly sample 15 scores from a population that is normally distributed with μ=230 and σ=50. What will be the standard deviation of the sample means (assuming you drew an infinite number of samples each with N=15)?
12.91
-Input the percent in question from the following image of a normal curve. Use the values given in the text from a similar sort of curve, do not include the % sign in your answer (Canvas expects a number). Percent = ____%
13.59
Now compute the 99% confidence interval from the same data. Y = 34, 23, 33, 29 Fill in the question mark: ? ≤ μ ≤
15.17
Y = 34, 23, 33, 29 SS=74.75 Step 3: estimate the standard error of the mean est. σM=?
2.4959
What values of z give a two-tail p value of .01 (.005 on each tail)
2.58 (p to z on oak software)
Compute the 95% confidence interval. Fill in the question mark: ? ≤ μ ≤
21.8
-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
Review: In which of the following experiments would you reject H0? Notice this is a 'select all that apply' question.
p=0.05 p<.001 p<.05 p=0.02
In an experiment to determine if plant growth is affected by whether chemical or organic fertilizer is used, the dependent variable would be:
plant growth
The sampling distribution of the mean is itself a:
population
When running an experiment what we actually have to base our decision upon are...
samples
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 __________ ___________ of the ___________
sampling distribution of the mean
How improbable the results have to be to reject H0 is called yourt
significance level
Now it is time to put the standard deviation on the curve, in this case it is the standard deviation of the possible values of (M1-M2). This is also known as the
standard error
Now it is time to put the standard deviation on the curve, in this case the standard deviation of the possible values of (M1-M2). This is also known as the
standard error
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 _________ __________ . (remember to put in 1 space between the two words, note term is singular, do not include the period in your answer)
standard score
Which of the following are attributes of a correlational design?
subjects are not randomly assigned to groups. The independent variable is not manipulated by the experimenter.
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
f μ1 - μ2 ≠ 0 which of the following do we conclude (assuming no confounding variables)
the independent variable has an effect
In Story Problem One (two-tailed test), t(6)=2.04, p=.0874 In Story Problem Two (one-tailed test), t(6)=2.04, p=.0437 Which approach had more power (assuming the IV really did have an effect)?
the one-tail test
So M1-M2=2.4. What can we conclude from that (without further analysis)?
the samples had different means
Which of the following is an assumption underlying the t test for independent groups?
the scores are independent of each other
Which of the following is an assumption underlying the t test for independent groups?
the two populations are normally distributed
Which of the following is an assumption underlying the t test for independent groups?
the two populations have the same variance
If the two populations have identical means:
the two sample means will probably differ at least a little due to random sampling error
The previous three probabilities were determined using the:
theoretical apprach
In some experiment M1=100 and M2=75, you analyze the data using a one-tailed test which predicted that μ1>μ2 and the results are statistically significant (i.e. you reject Ho). Which of the following can you conclude?
μ1>μ2
In some experiment M1=100 and M2=75, you analyze the data using a two-tailed test and the results are statistically significant (i.e. you reject Ho). Which of the following can you conclude?
μ1≠μ2
Which of the following would be the alternative hypothesis for this experiment?
μ1≠μ2
In some experiment M1=23 and M2=1750, you analyze the data using a one-tailed test which predicted that μ1>μ2 and the results are not statistically significant (i.e. you do not reject H0). Which of the following can you conclude?
μ1≤μ2
Which of the following is the symbol for the mean of the SDM?
μM
Which of the following is the symbol for the standard deviation of the SDM?
σM
A researcher wants to know what leads to better physical conditioning, downhill skiing or cross-country skiing. At the end of the winter she asks for volunteers who have only been downhill skiing during the winter and for volunteers who have been only cross country skiing during the winter. The physical conditioning of each volunteer is then measured. What type of experimental design is this?
correlational design
When determining cause and effect relationships between variables, the variable that you think will be the affected by the other variable is called the
dependent variable
Now let's say that the researcher is testing a theory which predicts that reaction times should be faster (i.e. smaller) to auditory stimuli than to visual stimuli. What type of hypothesis is being tested?
directional hypothesis
bSo t(8)=2.11, p=.0679, what is our decision about H0?
do no reject Ho
p=.1522, we will always use a significance level of .05, so what is the result of our experiment?
do not reject H0
M1=50 and M2=61 and the two-tailed p value is p=.09 For a one-tailed test of a theory which predicts that μ1 should be greater than μ2, p=.995, what is your decision?
do not reject HO
The 95% confidence interval is: -0.23 ≤ (μ1-μ2) ≤ 5.03 This is a range of plausible values for (μ1-μ2). H0 says that μ1=μ2 so (μ1-μ2)=0. That is in the range of plausible values. So what is our decision about H0?
do not reject HO
let's say that M1=50 and M2=61 and the two-tailed p value is p=.09 For the two-tailed test, what would you decide?
do not reject HO
p=.9563 What is your decision regarding H0?
do not reject HO
t(6)=2.04, p=.0874 What is your decision regarding H0?
do not reject HO
The previous probability was determined using the
empirical apprach
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
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
What has to be true for the theoretical approach to work?
every possible event has to have an equal chance of occuring
To say that the definition of two events cover every possible event that could occur would be to say that the events are ______________.
exhaustive
In Experiment One (with the original amount of additive) t(6)=2.04, p=.0874 In Experiment Three (with more additive) t(6)=2.717, p=.0348 Which experiment had more power (assuming the IV really did have an effect)?
experiment three
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 would lead to a more precise confidence interval of the effect size?
increase the size of the samples select a dependent variable that had less variance
Which of the following will increase the power of the experiment?
increasing N
This particular t test will only be appropriate when everyone's scores are completely unrelated to everyone else's scores, which is to say that the scores are __________.
independent
When determining cause and effect relationships between variables, the variable that you think will be the cause is called the ...
independent variable
According to the author, the main problem in using the mean to describe a group is that
it ignores the individual differences of the people within the group
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
To say that two events can't both happen is to say that they are ______ _____ events
mutually exclusive
The null and alternative hypotheses are always:
mutually exclusive Correct! exhaustive
Event A and Event ~A are:
mutually exclusive and exhaustive
The two hypotheses (H0 and Ha) are
mutually exclusive and exhaustive
If our decision is to 'not reject H0' can we conclude that H0 is true?
ni
If our decision is to 'not reject H0' can we conclude that the independent variable had no effect?
no
We are sampling 15 scores from a population, can we reasonably count on the SDM being normally distributed?
no
The researcher is simply testing to see if reaction times to the two different type of stimuli differ, she is not testing a theory which predicts which stimulus should have the faster reaction times. What type of hypothesis is being tested?
nondirectional hypothesis
'~A' represents.
not a
t(6)=2.04, p=.0874 The difference in mean gas mileage between the additive and nonadditive groups was...
not statistically significan
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 value
The researcher is testing a theory which predicts that reaction times should be faster (i.e. smaller) to auditory stimuli than to visual stimuli. Should the data be analyzed using a two-tailed test or a one-tailed test?
one-tailed
he probability of event 'A' occurring is symbolized as _______
p (a)
Which of the following is correct? Note I made this worth 5 points just because it is so important.
p is the probability that we would have obtained that big of a difference between the sample means if H0 were true.
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.
-Input the percent in question from the following image of a normal curve. Use the values given in the text from a similar sort of curve, do not include the % sign in your answer (Canvas expects a number). Percent = ____%
0.13
M1 - M2 ≠ 0. What can we conclude from that (without further analysis)? Select all that apply...
The samples had different means
If the null hypothesis is true, then the average (mean) value of (M1-M2) will equal...
0
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 and 100
M1=50 and M2=61 and the two-tailed p value is p=.09 For a one-tailed test of a theory which predicts that μ1 should be less than μ2 , what would be the one-tailed p value? p=? (don't round)
0.045
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
Which of the following would be the null hypothesis for this experiment?
μ1=μ2
Our answer to the previous question is our single, best, estimate of the mean of the population. It is unlikely to be exactly correct due to random sampling error. We would like to have an idea of just how far off that estimate might be. This is best approached through confidence intervals. We are going to compute the 95% confidence interval of the mean. Begin by computing the standard error of the mean, I will take you through the three steps, and give you the SS to start off with to cut down on your number crunching. Y = 34, 23, 33, 29 SS=74.75 Step 1: estimate the variance of the population. est. σ2=?
24.92
The process of computing the p value will be useful in later chapters. Now I'd like to switch to a different, but related, topic concerning "confidence intervals". Let's say that we sample four scores from a population and obtain the following data. Y = 34, 23, 33, 29 M=?
29.75
Y = 34, 23, 33, 29 Estimate the mean of the population from which we sampled. est. 𝝁=?
29.75
Y = 34, 23, 33, 29 df=?
3
Using the t tool, the values of t that cut off 5% of the curve (leaving the 95% in the center of the curve) are: t=± ? (input the positive value of t so that Canvas will grade it correctly) [On the t tool input the df, select the "p to t" function (as we will be inputting p and wanting t), select the two-tailed curve, and input p=.05.]
3.1824
-Estimate the standard deviation of the following curve.
3.2
Now estimate the standard deviation of the population from which we sampled. Y= 38, 39, 42, 44, 46 M=41.8 SS=44.80 est. σ=?
3.35
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
Compute the 95% confidence interval. Fill in the question mark: ≤ μ ≤ ?
37.69
We will need to use the t distribution tool in the Oak Software to get our p value, but first we need to compute the degrees of freedom. Y= 38, 39, 42, 44, 46 df=?
4
Y = 34, 23, 33, 29 SS=74.75 Step 2: estimate the standard deviation of the population. est. σ=?
4.99
We are sampling from a population that has 𝝁=40, what would be the average value of the sample means drawn from that population? In other words, 𝝁M=? [I highly recommend that you draw the SDM as we go along. Begin by drawing a curve, labeling it "The SDM for N=5", and then labeling the mean of the curve].
40
99% Confidence Interval Y = 34, 23, 33, 29 Fill in the question mark: ≤ μ ≤ ?
44.33
Which of the following confidence intervals provides a more precise idea of the effect of the independent variable in some experiment?
5.1 ≤ μ1-μ2 ≤ 8.9
Which of the following will have the greatest power?
A one-tail test when the theory's prediction is correct
If in reality H0 is false and your data lead you to not reject H0, what would that be?t
A type 2 errort
In which of the following samples did the scores differ more from each other? Assume there is no outlier affecting the measures.
Sample Two: S=741
Which of the following will increase the power of the experiment?
Decreasing the variability of the scores within each group
Which of the following will lead to more precise confidence intervals?
Drawing a large sample.
Which of the following will lead to more precise confidence intervals? Correct!
Drawing from a population that has a small variance.
Which of the following will increase the power of the experiment?
Increasing the effect of the independent variable
The 95% confidence interval is: 21.80 ≤ μ ≤ 37.69 Which of the following is the correct interpretation of this confidence interval?
It provides a range of plausible values for μ given our data.
The various approaches to increasing the power of the experiment will increase our chances of rejecting H0
Only if H0 is actually false
The various approaches to increasing the power of the experiment will increase our chances of proving our independent variable had an effect
Only when the independent variable really does indeed have an effect
The abbreviation for the sampling distribution of the mean is the '____'. (type the abbreviation in all caps).
SDM
So t(8)=2.11, p=.0679, we do not reject H0, which of the following can we say?
The difference between the sample means is not statistically significant
So t(8)=2.11, p=.004, we reject H0, which of the following can we say?
The difference between the sample means is statistically significant
So t(8)=2.11, p=.004, we reject H0. If we have no serious confounding variables then which of the following can we say?
The independent variable had an effect on the dependent variable
If μ1 - μ2 = 0 which of the following do we conclude (assuming no confounding variables)
The independent variable has no effect
Which of the following are attributes of a quasi-experimental design?
The independent variable is manipulated by the experimenter Subjects are not randomly assigned to groups.
Which of the following are attributes of a true experimental design?
The independent variable is manipulated by the experimenter. Subjects are randomly assigned to groups.
p(A|B) is read as...
The probability of event A given event B
So for our sample: est. μ = 29.75 and our 95% confidence interval is: 21.80 ≤ μ ≤ 37.69 (depending on how you rounded). Which of the following is the correct interpretation of this confidence interval?
There is a 95% chance that the confidence interval captures the true value of μ
How seriously is the validity of the t test threatened when the assumption of independence is violated?
Very seriously
So t(8)=2.11, p=.004, we reject H0, which of the following can we say?
We can conclude that the population means are different
So t(8)=2.11, p=.0679, we do not reject H0. If we have no serious confounding variables then which of the following can we say?
We cannot determine whether or not the independent variable had an effect on the dependent variable.
So t(8)=2.11, p=.0679, we do not reject H0, which of the following can we say?
We cannot determine whether or not the populations means are different.
-You sample 15 scores from a population that is normally distributed with μ=230 and σ=50. State the value of the standard error of the SDM. σM = ?
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"?t
When we have to estimate the standard deviation of the population.
The null and alternative hypotheses are always about:
populations
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
A researcher wants to know what leads to better physical conditioning, downhill skiing or cross-country skiing. What is the dependent variable of this experiment?
psychical education
A researcher wants to know what leads to better physical conditioning, downhill skiing or cross-country skiing. She obtains 30 volunteers who do not know how to ski, they are then allowed to select whether they would like to learn how to downhill ski or cross country ski. One group is taught how to downhill ski and subsequently go skiing 20 times during the winter, the other group is taught how to cross-country ski and they go skiing 20 times during the winter. At the end of the winter the physical conditioning of each student is measured. What type of experimental design is this?
quasi-experimental design
An experiment explores whether reaction times differ to an auditory stimulus (a tone) compared to a visual stimulus (flash of light). What is the dependent variable?
reaction times
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.t
reject
Which of the following are the only two possible (official) results of an experiment?
reject H0; do not reject H0
Let's say that our computations led to a different p value. t(8)=2.11, p=.004, what is our decision about H0?
reject HO
M1=50 and M2=61 and the two-tailed p value is p=.09 For a one-tailed test of a theory which predicts that μ1 should be less than μ2, p=.045, what is your decision?
reject HO
t(6)=2.04, p=.0437. What is your decision regarding H0?
reject HO
t(6)=2.717, p=.0348 What is your decision regarding H0?
reject HO
The 95% confidence interval is: -0.23 ≤ (μ1-μ2) ≤ 5.03 A researcher is testing a hypothesis that says that (μ1-μ2) should equal 7. What would be your decision about that hypothesis given the confidence interval?
reject that hypothesis
A researcher wants to know what leads to better physical conditioning, downhill skiing or cross-country skiing. She obtains 30 volunteers who do not know how to ski and randomly divides them into two groups. One group is taught how to downhill ski and subsequently go skiing 20 times during the winter, the other group is taught how to cross-country ski and they go skiing 20 times during the winter. At the end of the winter the physical conditioning of each student is measured. What type of experimental design is this?
true experimental design
Because we have to estimate the standard deviation (standard error) this means that the sampling distribution will be a '__' distribution rather than a 'normal' distribution. (don't input the '' signs).
ttttttttttt
The t test for two independent groups is an appropriate tool to use to analyze your data when you want to determine whether
two populations have different means
Please read the story problem ('Experiment One'). Given the way the story problem is worded, should this be analyzed as a two-tail or a one-tail test?
two-tail
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 value
The researcher is simply testing to see if reaction times to the two different type of stimuli differ, she is not testing a theory which predicts which stimulus should have the faster reaction times. Should the data be analyzed using a two-tailed test or a one-tailed test?
two-tailed
Given your decision to not reject H0, if you happen to be incorrect what type of error would that be:
type 2
In an experiment to determine if plant growth is affected by whether chemical or organic fertilizer is used, the independent variable would be:
type of fertilizer
A researcher wants to know what leads to better physical conditioning, downhill skiing or cross-country skiing. What is the independent variable of this experiment?
type of skiing
-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
If the 95% confidence interval of the effect size is: 2.89 ≤ μ1-μ2 ≤ 9.1, would we reject H0?
yes
If you have a confounding variable in your experiment and you reject H0 then..
you don't know whether the independent variable, the confounding variable or both caused the groups to differ
The assumption of normal populations can be (somewhat) safely violated if....
you have a large N in each group
If the null hypothesis is true, then the average (mean) value of M1-M2 should equal...
zero
Which of the following is the mean of the curve?
μ(M1-M2)=0
If the independent variable has an effect, then which of the following hypotheses would be true?
μ1 - μ2 ≠ 0
In a population that is normally distributed, what PERCENT of the scores will fall between z=-.40 and z=.40? This question is just to make sure you can go from proportion to percent. Do not include the percent sign, Take the answer to the full decimal places available. percent = __%
31.08%
What value of z gives a one-tail p value of .05 on the lower tail? z =
-1.65
What value of z gives a one-tail p value of .01 on the lower tail? z = ?
-2.33
-We sample 8 scores from a population that is normally distributed with a mean of μ=350 and a standard deviation of σ=20. What proportion of the sample means will be at least 17 above the population mean (i.e. M ≥ 367)? Recommendation: draw the SDM and shade in the regions. Answer to four decimal places.
0.0082
-We sample 8 scores from a population that is normally distributed with a mean of μ=350 and a standard deviation of σ=20. What proportion of the sample means will be at least 17 below the population mean (i.e. M ≤ 333)? Recommendation: draw the SDM and shade in the regions. Answer to four decimal places.
0.0082
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Look at the curve and estimate ('eyeball') the standard score for a score of 60 in that population.
-0.5
Using the formula for z, compute the standard score for a score of 60 in the population.
-0.56
-We sample 8 scores from a population that is normally distributed with a mean of μ=350 and a standard deviation of σ=20. What proportion of the sample means will be at least 17 away from the population mean in both directions (i.e. M ≤ 333 or M≥367)? Recommendation: draw the SDM and shade in the regions. Answer to four decimal places.
0.0164
What is the probability of drawing a 'one-eyed jack' from a deck of cards (there are two 'one-eyed' jacks in a deck of 52 cards)? p(A)=
0.0385
What is the probability of drawing a jack from a deck of cards (there are four jacks in a deck of 52 cards)? p(A)=
0.0769
-In a population that is normally distributed with a mean of 66 and a standard deviation of 5, what proportion of the scores will be at least 7 above the mean (i.e. Y≥73)?
0.080
In a population that is normally distributed, what proportion of the scores will fall 1.3 standard deviations or more above the mean (i.e. z ≥ 1.3)?
0.0968
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)=? (It would be an excellent idea to draw a curve and to show the formulas and your computations.)
0.1379 (σm=9/√6=3.67 z=-4/3.67=-1.09)
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'. p(A)=
0.17 (1/6; B doesnt matter)
In a population that is normally distributed, what proportion of the scores will fall at least 1.16 standard deviations away from the mean (in either direction)?
0.246
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)=? (It would be an excellent idea to draw a curve and to show the formulas and your computations.)
0.2758 ((σm=9/√6=3.67 z=-4/3.67=-1.09))
You have a bag of marbles consisting of 10 yellow, 5 green, 12 black, and 13 red marbles. Each marble has an equal chance of being selected. What is the probability you will draw a black marble? p(A)=
0.3
In a population that is normally distributed, what PROPORTION of the scores will fall between z=-.40 and z=.40? Take the answer out to the full decimal places available in the probability tool.
0.3108
-We have a population of scores that is normally distributed with a mean of μ=350 and a standard deviation of σ=20. What proportion of the scores fall within ±17 of the mean (i.e. 333 ≤ Y ≤ 367)? Recommendation: draw the population and shade in the regions. State answer to four decimal places.
0.6047
-input the percent in question from the following image of a normal curve. Use the values given in the text from a similar sort of curve, do not include the % sign in your answer (Canvas expects a number). Percent = ____%
2.15
What value of z gives a one-tail p value of .01 on the upper tail)? z = ?
2.33
-Input the percent in question from the following image of a normal curve. Use the values given in the text from a similar sort of curve, do not include the % sign in your answer (Canvas expects a number). Percent = ____%
34.13
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
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.
90
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 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
In the empirical approach why do you have to sample with replacement?
So that you sample from the same population each time
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
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
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
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 ____________ . Correct!
independent
What effect does a large amount of variability in the population have on the probability of getting a nonrepresentative sample?
makes it more likely
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
What has to be true for the empirical approach to work?
that you sample with replacement
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
We are sampling 40 scores from a population, can we reasonably count on the SDM being normally distributed?
yes
We are sampling 5 scores from a population that is normally distributed, can we reasonably count on the SDM being normally distributed?
yes
