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MATH 221 Exam 2 Review Flashcards | StudBud
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MATH 221 Exam 2 Review
MATH 221 Exam 2 Review
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1
What z-scores cut off the top 0.05% and bottom 0.05% of the distribution?
+/- 1.96
+/- 2.58
+/- 3.29
+/- 2.34
2
The Central Limit Theorem tells us that as samples get large enough...
the error is large
sampling distribution is skewed to the left
sampling distribution will have standard deviation equal to standard error
sampling distribution is skewed to the right
3
Which of the following is a Type II error?
false positive
you say someone is ill, but they are not
rejection of a true null hypothesis
false negative
4
The frequency distribution of the sample means from the same population is the...
normal distribution
frequency distribution
probability distribution
sampling distribution
5
99% of z-scores lie between...
+/- 3.29
+/- 2.34
+/- 2.58
+/- 1.96
6
The statistical model that we fit to our data represents...
the variance
the null hypothesis
the alternative hypothesis
the test statistic
7
When samples vary because they contain different members of the population, this is known as
sample mean
stratified sampling
random sampling
sampling variation
8
What threshold are we usually using (also called the significance level)?
0.05
0.10
0.01
0.02
9
If we took the mean of thousands of sample means from the same population, what would we get?
one of the sample means
the population mean
the sampling distribution
the standard error
10
A statistical model that tests a non-directional hypothesis is called a...
Type I error
two-tailed test
Type II error
one-tailed test
11
A negative deviance score tells us...
the mean is a good fit as a model
the mean is underestimating
the mean is overestimating
the mean is equal to the score
12
If the probability of obtaining the value of our test statistic by chance is less than 0.05, ...
we reject the null hypothesis
we have support for the null hypothesis
we have support for the alternative hypothesis
we reject the alternative hypothesis
13
A positive deviance score tells us...
the mean is underestimating
the mean is a good fit as a model
the mean is overestimating
the mean is equal to the score
14
What 2 ways have we learned to assess if the sample mean is representative of the population mean?
standard error & confidence intervals
standard error & test statistics
confidence intervals & effect size
standard deviation & confidence intervals
15
The standard deviation of sample means compared to the population mean is known as...
population mean
confidence intervals
standard error
central limit theorem
16
95% of z-scores lie between...
+/- 2.58
+/- 1.96
+/- 2.34
+/- 3.29
17
What equation do we use to construct the upper & lower bound of the 99% confidence interval?
X=\overline{X}\pm2.58\left(SE\right)
\sigma_{\overline{X}}=\frac{s}{\sqrt{n}}
Z=\frac{X-\overline{X}}{s}
X=\overline{X}\pm1.96\left(SE\right)
18
We calculate the probability that our model would fit the data if...
the alternative hypothesis is true
the standard error were small
the null hypothesis was rejected
the null hypothesis is true
19
The larger the test statistic is, ...
the less likely it is to occur by chance
the more likely it is to occur by chance
the more likely it is incorrect
the less likely it is incorrect
20
We can use the same probabilities for the tails of the distribution for a one- and two-tailed test.
False
True
21
Which of the following is non-directional hypothesis?
computer science & data science majors have different hair lengths
computer science majors have longer hair than data science majors
computer science & data science majors have the same hair length
22
What value do we need to calculate to find the probability of a particular score occuring in our distribution?
confidence interval
z-score
probability
standard error
23
What doe we call the boundaries within which we believe the true value of the mean will fall?
interquartile range
confidence intervals
min/max
standard error
24
How do we visually represent the deviance scores on a scatter plot of points when using the mean as the model?
horizontal line
a single point
vertical line
a vertical line for each point
25
Which of the following is a Type I error?
failure to reject a false null hypothesis
rejection of a true null hypothesis
false negative
someone is ill, but you tell them they're not
26
When you increase the sample size to create the illusion that something is significant, this is called...
effect size
statistical power
p-hacking
hypothesis testing
27
What value is the difference between each score in a dataset and the mean?
standard deviation
range
deviance score
mean
28
It doesn't matter if our model is accurate.
True
False
29
Test statistics are comparisons of...
null hypothesis to alternative hypothesis
standard error to confidence intervals
variance explained to variance not explained
effect to error
30
If our model is a good fit, then we'd expect it to be able to explain...
more variance than it can't explain
more error
the probability it occurred by chance alone
the null & alternative hypotheses
31
If dataset 1 has a SD of 1.73 and dataset 2 has a SD of 4.12, what does this tell us?
the mean is a better model for dataset 1
the mean is a better model for dataset 2
the mean is a bad model for both datasets
the mean is a good model for both datasets
32
The Central Limit Theorem tells us that as samples get large enough...
the sampling distribution will be normally distributed
the standard error gets large
the sample is representative of the population
the error goes to 0
33
If we're looking for the probability of a certain z-score or higher, which portion of the graph do we look at?
larger portion
smaller portion
34
The mean is the value that is closest to each of the scores (in a dataset) combined.
True
False
35
Confidence intervals are another way to assess the accuracy of the sample mean as an estimate of the population mean.
True
False
36
The more variation our model explains compared to what it can't, ...
the larger the model will be
the smaller the model will be
the larger the test statistic will be
the smaller the test statistic will be
37
The Central Limit Theorem tells us that as samples get large enough...
the standard devation gets large
the confidence interval gets large
the sampling distribution will have a mean equal to the population mean
the sample is not representative of the population
38
If we picked a number other than the mean to be our model, what value (calculated w/ our new number) would change & how?
variance would increase
standard deviation would increase
error would decrease
deviance scores would decrease
39
If the mean is 4.5 & the outcome for score #3 is 2, what is the error for score #3? outcome_i=\left(model\right)+error_i
6.5
-2.5
2.5
2.25
40
When considering the mean as a model, what value can be thought of as the average error between the mean & the scores?
variance
standard error
range
deviance score
41
As the probability decreases (from the previous question), we gain greater confidence in...
the sample mean being representative of the population mean
the alternative hypothesis
the null hypothesis
our confidence interval
42
What does large standard error tell us?
the mean is not a good fit as a model for our data
the sample mean is not representative of the population mean
the sample mean is representative of the population mean
the mean is a good fit as a model for our data
43
Which of the following can be used to assess if the mean as the model is a good fit for our data?
confidence intervals
mean
T-scores
standard deviation
44
The degree to which a statistical model represents the data collected is known as the...
standard error
statistical significance
confidence interval
fit of the model
45
We build statistical models from our data to...
make predictions
find the mean
compute deviance scores
46
If we take multiple samples from a population the means of each sample will be the same.
True
False
47
How do we visually represent the mean as a model on a scatter plot of points?
vertical line
a single point
horizontal line
a vertical line for each point
48
Does the mean have to be in our data set?
No
Yes
49
If we use the mean as a model for a dataset on income & our mean is $50,000 how much would we predict someone makes?
$25,000
$50,000
$60,000
$100,000
50
A statistical model that tests a directional hypothesis is called a...
Type I error
one-tailed test
Type II error
two-tailed test
51
99.9% of z-scores lie between...
+/- 3.29
+/- 2.58
+/- 2.34
+/- 1.96
52
Why do we need to compute the z-score?
b/c they tell us something about the sample size
b/c we like z-scores
b/c we want to compute more values using the z-scores
b/c we need our distribution to be normal
53
What z-scores cut off the top 0.5% and bottom 0.5% of the distribution?
+/- 3.29
+/- 2.58
+/- 1.96
+/- 2.34
54
What is the standardized measures of the size of an effect?
standard effect
statistical power
z-score
effect size
55
Since we want to say something about our population from our sample, we care if the sample is representative.
True
False
56
Which of the following is directional hypothesis?
computer science & data science majors have different hair lengths
computer science & data science majors have the same hair length
computer science majors have longer hair than data science majors
57
What is the probability of earning $95,000 or less if $95,000 has a z-score of 1.72?
4.272%
95.728%
95.637%
9.09%
58
Why do we use 0.05?
it's a simple benchmark
b/c of convention
it's arbitrary
all of the above
59
What z-scores cut off the top 2.5% and bottom 2.5% of the distribution?
+/- 1.96
+/- 2.58
+/- 2.34
+/- 3.29
