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