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1
Which of the following is a Type I error?
Failing to reject a false null hypothesis
Accepting a true alternative hypothesis
Rejecting a true null hypothesis
Failing to accept a false alternative hypothesis
2
A coin is flipped 5 times. What is the probability of getting exactly 3 heads?
5/32
10/32
3/5
15/32
3
Which data display is best for showing the distribution shape of a large numerical data set?
Bar graph
Histogram
Box plot
Pie chart
4
The mean score on a test is 80 with a SD of 5. If scores are normally distributed, what % of students score between
About 50%
About 68%
About 34%
About 95%
5
What type of variable is "number of siblings a student has"?
Nominal
Ordinal
Discrete
Continuous
6
What does a 95% confidence interval mean?
The interval includes 95% of the sample
95% of the data falls within the interval
There is a 95% chance any single data point is in the interval
We are 95% confident the population parameter is in the interval
7
What is the best way to reduce bias in a survey?
Only survey your friends
Increase the sample size and use random sampling
Ask leading questions
Use a convenience sample
8
A researcher divides students into grade levels, then randomly selects 10 students from each grade. What sampling method
Simple random sample
Cluster sample
Stratified sample
Systematic sample
9
What does the correlation coefficient (r) indicate in linear regression?
The slope of the regression line
The strength and direction of the linear relationship
10
What is the purpose of a chi-square test?
To find the mean of a dataset
To compare means between two groups
To measure correlation between variables
To test relationships between categorical variables
11
What does a probability of 0 mean?
Event will definitely happen
Event will happen sometimes
Event will never happen
Event might happen
12
If a confidence interval for the difference between two means includes zero, what does that imply?
The sample sizes are too small
The means are significantly different
The test was a chi-square test
The means are not significantly different
13
A 99% confidence interval is wider than a 95% confidence interval because:
It captures more uncertainty
It has a smaller margin of error
14
What does it mean if the p-value is less than alpha (0.05)?
Reject the null hypothesis
Increase the sample size
Accept the null hypothesis
The test is invalid
15
Which of the following conditions must be met to construct a valid confidence interval for a population mean?
The data must be approximately normally distributed or the sample size shou
The sample size must be less than 30
The population mean must be known
The sample data must be skewed
16
If r = -0.85, what does this indicate?
A weak positive correlation
No correlation
A strong positive correlation
A strong negative correlation
17
In a
normal distribution
, what percentage of data falls within one standard deviation of the mean?
68%
95%
34%
50%
18
Which of the following best describes a
simple random sample
?
Dividing the population into groups and randomly selecting one group
Surveying only friends and family
Every member of the population has an equal chance of being selected
Selecting every 10th person on a list
19
In a chi-square test, expected counts are calculated based on:
Observed data only
Sample means
Standard deviations
Assumed independence of variables
20
What does the slope in a linear regression equation represent?
The correlation coefficient
The strength of the relationship
The y-intercept
The change in y for a one-unit increase in x
21
What test would you use to compare the means of two independent groups?
Chi-square test
One-sample z-test
Two-sample t-test
ANOVA
22
Which of the following is
not
a necessary component of a well-designed experiment?
Census
Control group
Random assignment
Replication
23
In hypothesis testing, what does a p-value represent?
The probability that the null hypothesis is true
The probability of making a Type II error
The probability that the alternative hypothesis is false
The probability of obtaining a result at least as extreme as the one
24
What does R2R^2R2 (coefficient of determination) tell us?
The slope of the regression line
The proportion of variance in y explained by x
25
What effect does increasing the sample size have on the width of a confidence interval for a population proportion?
It has no effect
It decreases the width
It increases the width
It makes the interval less reliable
26
Which of the following is NOT an assumption of linear regression?
Independence of errors
Variables must be categorical
Linearity
Equal variance of errors (homoscedasticity)
27
What does a 95% confidence interval for a population mean indicate?
95% of the sample data falls within the interval
The sample mean is within 95% of the population mean
If we took many samples, about 95% of the calculated intervals would contai
There is a 95% chance that the population mean lies within the interval
28
What is a random variable ?
Take on all possible varuables
bronkitus of the hypotinuce
A green egg... What?
the sum of a number
29
When constructing a confidence interval for a population proportion, which condition must be met?
The sampling distribution of the sample proportion must be approximately nm
The population standard deviation must be known
The population must be normally distributed
The sample size must be greater than 30
30
What does r² (coefficient of determination) tell us?
The proportion of variation in y explained by x
The strength of the linear relationship
The direction of the relationship
The correlation coefficient squared
31
What is the probability of rolling a 4 on a fair six-sided die?
1/6
1/3
1/2
1/4
32
When should a t-distribution be used instead of a normal distribution in inference about a population mean?
When the data are categorical
When the sample size is large (n > 30)When the population standard deviatio
When the population standard deviation is unknown and the sample size is sm
When the population standard deviation is known
33
What does This mean "Mew"
To put the tongue on the roof of the mouth
The sound a cat makes
The sum or the answer
The mean of the population
34
A researcher divides students into grade levels, then randomly selects 10 students from each grade. What sampling method
Stratified sample
Systematic sample
Simple random sample
Cluster sample
35
Which of the following is
not
a necessary component of a well-designed experiment?
. Random assignment
Census
Replication
Control group
36
If the residuals from a linear regression are randomly scattered around zero, what does this suggest?
The slope is zero
The model does not fit the data well
There is a nonlinear relationship
The model fits the data well
37
Which situation best fits using a
linear model
?
The population of a city over time (exponential growth)
The distance a ball travels vs. time in the air (parabolic)
Temperature over a year (cyclical)
The relationship between height and shoe size
38
In hypothesis testing, the p-value represents
The probability of observing the data assuming the null hypothesis is true
The significance level of the test
The probability of the alternative hypothesis being true
The probability that the null hypothesis is true
39
In a box plot, which values are used to create the box?
First quartile and third quartile
Median and mode
Mean and standard deviation
Minimum and maximum
40
Which of the following increases the power of a hypothesis test for a population mean?
Increasing the significance level (alpha)
. Increasing the variability in the data
Decreasing the sample size
Using a two-tailed test instead of a one-tailed test
41
What is the range of the correlation coefficient (r)?
-1 to 1
0 to 100
0 to 1
-∞ to ∞
42
What is the significance level (alpha) typically set at in hypothesis testing?
0.05
0.01
0.50
0.10
43
Which of the following is the
median
of the data set: 8, 12, 15, 18, 22?
18
14
15
12
44
What does the interquartile range (IQR) represent?
The spread of the entire data set
The difference between the highest and lowest value
The range of the middle 50% of the data
The average value in a data set
45
Which of the following is a type of chi-square test?
Chi-square test for regression
Chi-square test for independence
Chi-square test for correlation
Chi-square test for means
46
In the regression equation y=mx+by = mx + by=mx+b, what does mmm represent?
The correlation coefficient
The slope of the line
The y-intercept
47
Which sampling method divides the population into groups and then randomly selects entire groups?
Stratified sampling
Cluster sampling
48
What is the main difference between an
observational study
and an
experiment
?
Observational studies use a control group
Observational studies manipulate variables
Only experiments use statistics
Experiments randomly assign treatments
49
In hypothesis testing for a population mean, what is the null hypothesis typically stating?
The sample mean is equal to the population mean
The population mean is equal to a specified value
The population mean is greater than a specified value
The population mean is less than a specified value
50
In the equation of a line of best fit, what does the
slope
represent?
The starting value
The predicted value of y when x is 0
The change in y for a one-unit increase in x
The midpoint of the data set
51
Which type of bias occurs when people choose whether or not to participate?
Undercoverage bias
Nonresponse bias
Voluntary response bias
Response bias
52
In a stratified sample, the population is divided into
The largest possible groups
Strata based on shared characteristics
Random groups
Groups of volunteers
53
What is the null hypothesis in a chi-square test for independence?
The variables are independent
There is a strong correlation
There is a difference in means
The variables are dependent
54
What is the probability of flipping exactly 2 heads in 3 fair coin tosses?
3/8
1/2
55
Which measure of center is most affected by extreme outliers?
mean
range
median
mode
56
Which of the following is an example of a
qualitative
variable?
the numbers of hours you work.
age
the amount of candy you have
My lizards color
57
A student recorded the number of hours they studied each night for a week:
7
6
4
5
58
What is the
range
of the data set: 10, 20, 30, 40, 50?
60
50
40
30
59
What assumption is important for a two-sample t-test?
Samples are dependent
Data must be categorical
Samples must be paired
Samples have equal variances
60
What is a voluntary response sample?
Participants selected by a computer
Participants chosen at random
Participants who choose to respond on their own
Participants selected by the researcher
61
If 40% of students like basketball and 60% like soccer, what is the chance a random student likes both
60%
40%
100%
Needs more information
62
What is X bar
Mew
The statistic
The sample mean
The mean
63
What is the purpose of a confidence interval in statistics?
To display the distribution of sample data
To test the correlation between two variables
To estimate the range of possible values for a population parameter
To determine the exact value of a population parameter
64
What is the purpose of a paired t-test?
To analyze categorical data
To test for correlation between two variables
To compare two independent samples
To compare means from the same group at two different times
65
Which type of bias occurs when certain groups are underrepresented in a survey?
Response bias
Sampling bias
Measurement bias
Confirmation bias
66
What does a large chi-square statistic indicate?
Little difference between observed and expected counts
The variables are independent
The sample size is too small
Strong evidence against the null hypothesis
67
If a Conf Int for a population mean doesn't have 50, what can we learn about a hypoth test with a null hypoth that
We reject the null hypothesis
We accept the null hypothesis
The test is inconclusive
We fail to reject the null hypothesis
68
What is a simple random sample?
Picking people based on convenience
Selecting a sample where each individual has an equal chance to be chosen
Choosing every 3rd person from a list
Sampling only people who volunteer
69
What does a
correlation coefficient (r)
of -0.89 indicate?
A strong negative linear relationship
A perfect positive linear relationship
A weak positive linear relationship
No linear relationship
70
What is the purpose of a linear regression model?
To calculate the mean of a dataset
To predict the value of a dependent variable based on an independent variab
To describe the relationship between two categorical variables
To find the mode of the data
