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Statistics Final
Statistics Final
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1
Which of the following best describes the shape of a standard normal distribution?
Uniform
Skewed right
Skewed left
Bell-shaped and symmetric
2
What does a small p-value indicate in the context of a hypothesis test?
A large sample size
The data is not random
The null hypothesis is true
Strong evidence against the null hypothesis
3
In a standard normal distribution, what is the probability that a value is greater than z = 0?
0.5
0
0.25
1
4
Which of the following is a valid probability distribution?
All probabilities are between 0 and 1, and sum to 1
All probabilities are negative
Probabilities sum to 2
One value has a probability over 1
5
Which of the following statistics is not resistant to outliers?
Median
Mode
Mean
Interquartile Range (IQR)
6
What happens to the margin of error if you increase the confidence level from 90% to 95%?
It increases
It decreases
It stays the same
It becomes 0
7
When describing the distribution of a quantitative variable, which of the following is not typically included?
Center
Shape
Spread
Cause
8
Which of the following is a categorical variable?
Age in years
Type of pet owned
Number of siblings
Height in inches
9
In a normal distribution, what percent of data falls within one standard deviation of the mean?
About 75%
About 95%
About 50%
About 68%
10
If the p-value of a significance test is 0.03 & the chosen significance level α is 0.05, what conclusion should be made?
Cannot determine
Increase the sample size
Fail to reject the null hypothesis
Reject the null hypothesis
11
The mean of the sampling distribution of the sample mean is equal to:
The sample standard deviation
The sample mean
The population mean
The population standard deviation
12
A bag contains 4 white, 5 tan, and 6 red balls. One ball is drawn at random. What is the probability that it is not tan?
1/3
5/15
2/3
4/5
13
Which of the following conditions must be checked before performing a one-sample t-test for a mean?
Normal population, Known standard deviation, Randomness
Independence, Equal variances, Normality
Large sample size, Skewness, Outliers
Randomness, Normality, Independence
14
If a 1 sided z-test for a population proportion yields a p-value of 0.03, which is a correct interpretation?
There is a 3% chance the null hypothesis is true
The sample proportion differs from the population proportion by 3%
There is a 3% chance of making a Type II error
Prob of observing a sample proportion is extreme or more extreme. null=3%
15
Which of the following graphs is most appropriate for displaying the distribution of a single quantitative variable?
Segmented bar graph
Pie chart
Bar chart
Histogram
16
What does it mean to be “95% confident” in the context of a confidence interval?
About 95% of intervals will capture the true population proportion
There is a 95% chance the sample proportion is correct
The true proportion is guaranteed to be in the interval
The sample proportion is within 95% of the true value
17
What is the purpose of a chi-squared goodness-of-fit test?
To test whether two population means are equal
Determine if a categorical variable is associated with a numerical variable
To compare proportions from two independent samples
To see if observed categorical data matches an expected distribution
18
Which of the following would result in a wider confidence interval for a population proportion?
A smaller margin of error
A smaller sample size
A larger sample size
A lower confidence level
19
Which of the following p-values would lead to rejecting the null hypothesis at the 0.05 significance level?
0.10
0.06
0.01
0.08
20
Which of the following increases the margin of error in a confidence interval for a mean?
Increasing the standard deviation
Decreasing the confidence level
Using a z-distribution
Increasing the sample size
21
Which of the following is true of all density curves?
They must be symmetric
The mean and median are always the same
The total area under the curve is 1
They must follow a normal distribution
22
Two coins are tossed. What is the probability of getting at least one head?
3/4
1/4
1/2
1
23
What is the purpose of random assignment in an experiment?
To reduce the effects of confounding variables
To ensure a representative sample
To match treatment and control groups
To reduce variability
24
If a distribution is right-skewed, which of the following is most likely true?
The mean is greater than the median
The median is greater than the mode
The mean is less than the median
The mean and median are equal
25
Why do we use a residual plot when assessing a linear model?
To calculate the correlation
To visualize the mean of the data
To confirm the variables are quantitative
To check whether a linear model is appropriate
26
As sample size increases, what happens to the standard deviation of the sampling distribution of the sample mean?
It increases
It decreases
It becomes 0
It stays the same
27
In a well-designed experiment, random assignment of treatments helps to:
Eliminate response bias
Ensure a representative sample
Create similar groups and reduce confounding
Reduce sampling error
28
Which condition must be met to perform a one-sample t-test?
Data must be categorical
Population must be normal or n ≥ 30
Proportions must match
Variances must be equal
29
Which of the following statements is true about the standard normal distribution?
It has a mean of 1 and a standard deviation of 0
It contains no outliers
It is skewed right
It has a mean of 0 and standard deviation of 1
30
A distribution with a long right tail is described as:
Skewed left
Symmetric
Bimodal
Skewed right
31
What is the shape of the sampling distribution of the sample mean when the sample size is large?
Uniform
Bimodal
Approximately normal
Skewed right
32
Which of the following is true about a continuous random variable?
Probability that the variable takes on any single exact value is always 1.
The sum of the probabilities of all possible values is 1
The probability that the variable takes on any single exact value is 0
The variable can take only integer values
33
If a population is normal, what can be said about the sampling distribution of the sample mean for any sample size?
It will be exactly normal
It will be approximately normal only if n≥30n \ge 30n≥30
It will be uniform
It will be skewed
34
Which of the following conditions must be checked before performing inference for linear regression?
Linearity, normality, independence, equal standard deviations
Randomness, equal sample sizes, normality
Equal standard deviations, large sample size, no outliers
Explanatory variable must be categorical &the response must be quantitative
35
A chi-squared test for independence is used when:
Testing whether two categorical variables are related
Comparing two means
Comparing a sample mean to a population mean
Testing whether a sample proportion equals a population proportion
36
When using a two-sample t-test for means, which assumption must be true?
Both groups must have the same mean
Each sample is randomly selected and independent of the other
The samples are from the same population
The samples are dependent
37
Which of the following affects the standard error of a sample mean?
Median
Sample mean
Population size
Sample size
38
What does a z-score represent?
The average of a data set
The number of standard deviations a value is from the mean
The total area under a normal curve
The median of a data set
39
If an event has probability 0.8, what is the probability of its complement?
0
0.8
1
0.2
40
The slope of the least-squares regression line is:
The correlation coefficient
The residual
The change in y per unit change in x
The intercept
41
Which of the following is a condition that must be met before using a chi-squared test?
The sample size must be less than 30
All expected counts must be at least 5
The population must be normally distributed
All expected counts must be greater than or equal to 30
42
Which of the following does NOT describe a binomial setting?
Each trial has only two possible outcomes
The probability of success changes from trial to trial
There are a fixed number of trials
Trials are independent
43
What type of data is required for a chi-squared goodness-of-fit test?
Categorical data
Numerical data
Proportions from independent samples
Paired data
44
Which situation would most appropriately use a paired t-test?
Testing a proportion in a single population
Measuring student test scores before and after a tutoring program
Comparing the means of two independent groups
Estimating a population mean with known standard deviation
45
Which condition must be checked before constructing a confidence interval for a proportion?
Equal variances
Large Counts: np ≥ 10 and n(1−p) ≥ 10
Sample mean > population mean
Normally distributed data
46
Which of the following scatterplots indicates a nonlinear relationship?
A straight upward-sloping trend
A curved upward trend
A line sloping downward
A cloud of points with no pattern
47
A fair die is rolled twice. Let X be the sum of the two rolls. What is the expected value of X?
8
5
6
7
48
A survey is posted on a school’s website asking for opinions on school lunch. What type of bias is most likely present?
Undercoverage
Nonresponse bias
Response bias
Voluntary response bias
49
A die is rolled once. What is the probability of getting an odd number?
1/6
1/2
1/3
2/3
50
The degrees of freedom for a chi-squared test for independence in a two-way table are calculated as:
n−1
rc
r+c−2
(r−1)(c−1)
51
A matched-pairs design requires:
Two independent samples
Random sampling from each group
Equal sample sizes
Two measurements on the same subject
52
Which of the following is true about the correlation coefficient r?
It measures the strength and direction of a linear relationship
It proves causation
It is always positive
It can be greater than 1
53
What is the probability of flipping two heads in a row with a fair coin?
1/2
1/4
1/3
3/4
54
A two-sided test yields a p-value of 0.08. If the significance level is 0.05, what conclusion should be made?
Reject the null hypothesis; the p-value is less than 0.10
Accept the null hypothesis; the p-value is too high
Fail to reject the null hypothesis; the evidence is not strong enough
Reject the null hypothesis; there is strong evidence against it
55
Which of the following conditions must be checked before conducting a one-proportion z-test?
The sample size is less than 10% of the population
The number of expected successes and failures is at least 10
The sample mean is normally distributed
The population is normally distributed
56
Which of the following is a discrete random variable?
The time it takes to run a mile
The number of heads in 3 coin tosses
The exact height of a randomly chosen student
The weight of a watermelon
57
The standard deviation of the sampling distribution of the sample mean is called:
Margin of error
Sampling error
Population standard deviation
Standard error
58
Which of the following indicates the strongest linear relationship?
r=−0.34
r=−0.89
r=0.15
r=0.72
59
What does a confidence interval for the slope of the regression line tell us?
Range in which individual predicted values will fall with 95% confidence
The prediction interval for future data points
The range of all possible correlation values for the data
Range of plausible values for the true population slope of regression line
60
A student scores in the 85th percentile on a standardized test. What does this mean?
The student scored worse than 85% of all test-takers
The student scored better than 85% of all test-takers
The student got 85% of the questions correct
The student scored in the top 15% of the class
61
In a study examining how hours studied affect exam scores, which is the explanatory variable?
The residuals
The correlation coefficient
Hours studied
Exam scores
62
Why is a control group important in an experiment?
To eliminate the placebo effect
To ensure every subject receives treatment
To reduce variability in the population
To allow comparison to a group not receiving the treatment
63
Which of the following will reduce the margin of error in a t-test for a population mean?
Decreasing the sample size
Increasing the confidence level
Increasing the sample size
Using a larger t-score
64
Which of the following will make a confidence interval
wider
, assuming all other factors remain the same?
Decreasing the confidence level
Increasing the sample size
Increasing the standard deviation
Decreasing the margin of error
65
If two events A and B are independent, which of the following is true?
P(A ∩ B) = P(A) × P(B)
P(A ∩ B) = 0
P(A ∩ B) = P(A) + P(B)
P(A ∪ B) = P(A) × P(B)
66
If a 95% confidence interval for a population mean is (12.4, 15.8), what does this mean?
We are 95% confident the true mean lies between 12.4 and 15.8
The mean of the sample is 14.1
The probability the mean is in that interval is 95%
95% of the data falls between 12.4 and 15.8
67
If you want to reduce the margin of error in a confidence interval for a proportion, what should you do?
Both A and C
Use a lower confidence level
Decrease the sample size
Increase the sample size
68
A box contains 5 red balls and 3 blue balls. One ball is drawn at random. What is the probability that it is blue?
3/5
3/8
5/8
1/2
69
As the sample size increases, the sampling distribution of the sample mean becomes:
Skewed to the right
Less variable
Less normal
More variable
70
A correlation of r=−0.95 suggests:
No association
A strong negative association
A weak negative association
A strong positive association
