Togus Bash
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Togus Bash
STATISTICS
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Probability Distributions
In an exponential distribution, what is the cumulative distribution function?
A. F(x) = 1 - e^(-?x).
B. F(x) = (?^x * e^(-?)) / x!.
C. F(x) = (1/sv(2p)) * e^(-(x-?)^2 / (2s^2)).
D. F(x) = p * (1-p)^(x-1.
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the normal approximation to the binomial distribution when n is large and p is close to 0
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution skewed.
Togus Bash
STATISTICS
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Probability Distributions
In a Poisson distribution, what is the variance?
A. ?.
B. 1/?.
C. ?^2.
D. v?.
Togus Bash
STATISTICS
-
Probability Distributions
What is the relationship between the normal and lognormal distributions?
A. Lognormal distribution is the logarithm of a normal distribution.
B. Normal distribution is the logarithm of a lognormal distribution.
C. There is no relationship between the two distributions.
D. Lognormal distribution is always normal.
Togus Bash
STATISTICS
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Probability Distributions
In a hypergeometric distribution, what is the variance?
A. n * (N-n) * (N-n-1) / (N^2 * (N-1)).
B. n * (N-n) / N.
C. n * p * (1-p).
D. n * (1-p).
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the Poisson approximation to the binomial distribution when n is large and p is small?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution normal.
Togus Bash
STATISTICS
-
Probability Distributions
In a geometric distribution, what is the variance?
A. p/(1-p).
B. 1/p.
C. (1-p)/p^2.
D. p^2/(1-p)^2.
Togus Bash
STATISTICS
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Probability Distributions
What is the relationship between the Poisson and exponential distributions?
A. Poisson distribution models the number of events in a fixed interval, while exponential distribution models the time between events.
B. Poisson distribution is always exponential.
C. Exponential distribution is always Poisson.
D. There is no relationship between the two distributions.
Togus Bash
STATISTICS
-
Probability Distributions
In a normal distribution, what is the probability density function?
A. f(x) = (1/sv(2p)) * e^(-(x-?)^2 / (2s^2)).
B. f(x) = ? * e^(-?x).
C. f(x) = (?^x * e^(-?)) / x!.
D. f(x) = p * (1-p)^(x-1).
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the Central Limit Theorem in the context of probability distributions?
A. To show that the sampling distribution of the mean approaches a normal distribution as the sample size increases.
B. To prove that all probability distributions are normal.
C. To simplify calculations involving probability distributions.
D. To make inferences about population parameters.
Togus Bash
STATISTICS
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Probability Distributions
In a binomial distribution, what is the expected number of successes?
A. n * p.
B. n * (1-p).
C. n * (n-1) * p^2.
D. n * (n-1) * p * (1-p).
Togus Bash
STATISTICS
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Probability Distributions
What is the relationship between the normal and exponential distributions?
A. Exponential distribution is the reciprocal of a normal distribution.
B. Normal distribution is the reciprocal of an exponential distribution.
C. There is no relationship between the two distributions.
D. Exponential distribution approaches normal distribution as the rate parameter increases.
Togus Bash
STATISTICS
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Probability Distributions
In a hypergeometric distribution, what is the expected number of successes?
A. n * (N-n)/N.
B. n * p.
C. n * (1-p).
D. n * (N-n).
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the lognormal distribution?
A. To model variables that are the product of many independent random variables.
B. To model variables that are the sum of many independent random variables.
C. To model variables that are always positive.
D. To model variables that are always negative.
Togus Bash
STATISTICS
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Probability Distributions
In a Poisson distribution, what is the probability mass function?
A. P(X=x) = ?^x * e^(-?) / x!.
B. P(X=x) = (n!/(x!(n-x)!)) * p^x * (1-p)^(n-x).
C. P(X=x) = (1/sv(2p)) * e^(-(x-?)^2 / (2s^2)).
D. P(X=x) = p * (1-p)^(x-1).
Togus Bash
STATISTICS
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Probability Distributions
What is the relationship between the normal and uniform distributions?
A. Uniform distribution approaches normal distribution as the range increases.
B. Normal distribution is always uniform.
C. Uniform distribution is always normal.
D. There is no relationship between the two distributions.
Togus Bash
STATISTICS
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Probability Distributions
In a geometric distribution, what is the expected number of failures before the first success?
A. 1/p.
B. p.
C. 1-p.
D. p/(1-p).
Togus Bash
STATISTICS
-
Probability Distributions
What is the purpose of the normal approximation to the binomial distribution?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution skewed.
Togus Bash
STATISTICS
-
Probability Distributions
In an exponential distribution, what is the probability density function?
A. f(x) = ? * e^(-?x).
B. f(x) = (?^x * e^(-?)) / x!.
C. f(x) = (1/sv(2p)) * e^(-(x-?)^2 / (2s^2)).
D. f(x) = p * (1-p)^(x-1).
Togus Bash
STATISTICS
-
Probability Distributions
What is the relationship between the mean and variance in a Poisson distribution?
A. Mean is always greater than variance.
B. Variance is always greater than mean.
C. Mean and variance are always equal.
D. Mean and variance are always 1.
Togus Bash
STATISTICS
-
Probability Distributions
In a hypergeometric distribution, what is the probability mass function?
A. P(X=x) = (C(n,x) * C(N-n,n-x)) / C(N,n).
B. P(X=x) = (n!/(x!(n-x)!)) * p^x * (1-p)^(n-x).
C. P(X=x) = ?^x * e^(-?) / x!.
D. P(X=x) = p * (1-p)^(x-1).
Togus Bash
STATISTICS
-
Probability Distributions
What is the purpose of the Poisson approximation to the binomial distribution when n is large and p is small?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution normal.
Togus Bash
STATISTICS
-
Probability Distributions
In a geometric distribution, what is the probability mass function?
A. P(X=x) = p * (1-p)^(x-1).
B. P(X=x) = (1-p)^(x-1) * p.
C. P(X=x) = p^x * (1-p)^(n-x).
D. P(X=x) = n!/(x!(n-x)!) * p^x * (1-p)^(n-x).
Togus Bash
STATISTICS
-
Probability Distributions
What is the relationship between the normal and lognormal distributions?
A. Lognormal distribution is the logarithm of a normal distribution.
B. Normal distribution is the logarithm of a lognormal distribution.
C. There is no relationship between the two distributions.
D. Lognormal distribution is always normal.
Togus Bash
STATISTICS
-
Probability Distributions
In a binomial distribution, what is the probability mass function?
A. P(X=x) = n!/(x!(n-x)!) * p^x * (1-p)^(n-x).
B. P(X=x) = ?^x * e^(-?) / x!.
C. P(X=x) = (N-n)!/(x!(n-x)!) * p^x * (1-p)^(n-x).
D. P(X=x) = (N!/(x!(N-x)!)) * p^x * (1-p)^(N-x).
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the Poisson process?
A. To model the number of events in a fixed interval of time or space.
B. To model the time between events.
C. To model the number of events in a continuous time interval.
D. To model the number of events in a discrete time interval.
Togus Bash
STATISTICS
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Probability Distributions
In a normal distribution, what does the 95% confidence interval represent?
A. 95% of the data lies within the interval.
B. 95% of the population lies within the interval.
C. 95% of the time the sample mean will fall within the interval.
D. 95% of the time the population mean will fall within the interval.
Togus Bash
STATISTICS
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Probability Distributions
What is the relationship between the mean and variance in an exponential distribution?
A. Mean is always greater than variance.
B. Variance is always greater than mean.
C. Mean and variance are always equal.
D. Mean and variance are not necessarily equal.
Togus Bash
STATISTICS
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Probability Distributions
In a hypergeometric distribution, what is the main assumption?
A. Sampling is done with replacement.
B. Sampling is done without replacement.
C. Population size is infinite.
D. Events occur independently.
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the Poisson approximation to the binomial distribution?
A. To simplify calculations.
B. To make the binomial distribution discrete.
C. To make the binomial distribution continuous.
D. To make the binomial distribution normal.
Togus Bash
STATISTICS
-
Probability Distributions
In an exponential distribution, what does the parameter ? represent?
A. Mean.
B. Variance.
C. Standard deviation.
D. Rate parameter.
Togus Bash
STATISTICS
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Probability Distributions
What is the relationship between the normal and binomial distributions?
A. Binomial distribution approaches normal distribution as n increases and p is close to 0.5.
B. Binomial distribution is always normal.
C. Normal distribution is always binomial.
D. There is no relationship between the two distributions.
Togus Bash
STATISTICS
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Probability Distributions
In a geometric distribution, what is the expected number of trials until the first success?
A. 1/p.
B. p.
C. 1-p.
D. p/(1-p).
Togus Bash
STATISTICS
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Probability Distributions
What is the main assumption of the Poisson distribution?
A. Events occur independently.
B. Events occur at a constant rate.
C. Events occur in continuous time.
D. Events occur in discrete time.
Togus Bash
STATISTICS
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Probability Distributions
In a normal distribution, what does the 68-95-99
A. 68% of data lies within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.
B. 95% of data lies within 1 standard deviation, 99.7% within 2 standard deviations, and 99.9% within 3 standard deviations.
C. 68% of data lies within 1 standard deviation, 95% within 3 standard deviations, and 99.7% within 5 standard deviations.
D. 95% of data lies within 1 standard deviation, 99.7% within 2 standard deviations, and 99.9% within 4 standard deviations.
Togus Bash
STATISTICS
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Probability Distributions
Which of the following is a continuous probability distribution?
A. Binomial distribution.
B. Poisson distribution.
C. Exponential distribution.
D. Hypergeometric distribution.
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the Central Limit Theorem?
A. To describe the shape of a distribution.
B. To make inferences about population parameters.
C. To determine the sampling distribution of the mean.
D. To calculate probabilities.
Togus Bash
STATISTICS
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Probability Distributions
In a geometric distribution, what does the parameter p represent?
A. Probability of success in a single trial.
B. Probability of success in multiple trials.
C. Number of trials.
D. Number of failures.
Togus Bash
STATISTICS
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Probability Distributions
What is the relationship between the mean and standard deviation in a normal distribution?
A. Mean is always greater than standard deviation.
B. Mean is always less than standard deviation.
C. Mean and standard deviation are always equal.
D. Mean and standard deviation are not necessarily equal.
Togus Bash
STATISTICS
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Probability Distributions
Which of the following is a property of the Poisson distribution?
A. Mean is always greater than variance.
B. Variance is always greater than mean.
C. Mean and variance are always equal.
D. Mean and variance are not necessarily equal.
Togus Bash
STATISTICS
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Probability Distributions
What is the purpose of the standard normal distribution?
A. To standardize data.
B. To make predictions about populations.
C. To analyze data from samples.
D. To summarize data.
Togus Bash
STATISTICS
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Probability Distributions
In a normal distribution, what is the relationship between the mean and median?
A. Mean is always greater than median.
B. Mean is always less than median.
C. Mean and median are always equal.
D. Mean and median are not necessarily equal.
Togus Bash
STATISTICS
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Probability Distributions
What is the main characteristic of a binomial distribution?
A. Continuous.
B. Discrete.
C. Symmetric.
D. Skewed.
Togus Bash
STATISTICS
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Probability Distributions
Which of the following is a discrete probability distribution?
A. Normal distribution.
B. Exponential distribution.
C. Poisson distribution.
D. Uniform distribution.
Togus Bash
STATISTICS
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Probability Distributions
What is the primary purpose of probability distributions?
A. To describe the likelihood of events.
B. To make predictions about populations.
C. To analyze data from samples.
D. To summarize data.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of a regression coefficient?
A. To indicate the strength and direction of a relationship.
B. To summarize data.
C. To test hypotheses.
D. To calculate means.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is an assumption of linear regression?
A. Homoscedasticity.
B. Multicollinearity.
C. Independence of errors.
D. All of the above.
Togus Bash
STATISTICS
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Inferential Statistics
What does a 95% confidence interval mean?
A. 95% of the sample data falls within the interval.
B. We are 95% confident the population parameter is within the interval.
C. The interval will contain the parameter 95% of the time.
D. 95% chance of making a Type I error.
Togus Bash
STATISTICS
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Inferential Statistics
What is the main purpose of bootstrapping in statistics?
A. To estimate the sampling distribution.
B. To increase sample size.
C. To reduce bias.
D. To visualize data.
Togus Bash
STATISTICS
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Inferential Statistics
In a two-sample t-test, what assumption is made about the variances?
A. They are equal.
B. They are unequal.
C. They are both zero.
D. They are both one.
Togus Bash
STATISTICS
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Inferential Statistics
What does a confidence interval of (10, 20) imply?
A. The population mean is exactly 15.
B. The population mean is between 10 and 20.
C. The sample mean is between 10 and 20.
D. The population mean is less than 10.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of a sample in inferential statistics?
A. To represent the entire population.
B. To summarize data.
C. To test hypotheses.
D. To collect data.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following tests is used for paired samples?
A. Independent t-test.
B. Paired t-test.
C. ANOVA.
D. Chi-square test.
Togus Bash
STATISTICS
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Inferential Statistics
What does the term "effect size" refer to?
A. The magnitude of a relationship.
B. The direction of a relationship.
C. The sample size.
D. The significance level.
Togus Bash
STATISTICS
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Inferential Statistics
What is the main goal of a regression analysis?
A. To predict outcomes.
B. To summarize data.
C. To visualize data.
D. To test hypotheses.
Togus Bash
STATISTICS
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Inferential Statistics
In regression analysis, what does multicollinearity refer to?
A. High correlation between independent variables.
B. Low correlation between independent variables.
C. High correlation between dependent variables.
D. No correlation at all.
Togus Bash
STATISTICS
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Inferential Statistics
What does a high p-value indicate?
A. Strong evidence against the null hypothesis.
B. Weak evidence against the null hypothesis.
C. Strong evidence for the null hypothesis.
D. No evidence at all.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of the Bonferroni correction?
A. To adjust for multiple comparisons.
B. To increase power.
C. To decrease sample size.
D. To improve accuracy.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is an example of a Type II error?
A. Failing to reject a false null hypothesis.
B. Rejecting a true null hypothesis.
C. Accepting a true alternative hypothesis.
D. Rejecting a false alternative hypothesis.
Togus Bash
STATISTICS
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Inferential Statistics
What is the main characteristic of non-parametric tests?
A. They do not assume a normal distribution.
B. They require large sample sizes.
C. They are always more powerful than parametric tests.
D. They can only be used with categorical data.
Togus Bash
STATISTICS
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Inferential Statistics
In hypothesis testing, what does it mean to "reject the null hypothesis"?
A. Conclude there is an effect.
B. Conclude there is no effect.
C. Accept the null hypothesis.
D. None of the above.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of a scatter plot in regression analysis?
A. To visualize the relationship between two variables.
B. To summarize categorical data.
C. To show frequency distribution.
D. To calculate means.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is a limitation of inferential statistics?
A. Requires random sampling.
B. Assumes normality.
C. Sensitive to outliers.
D. All of the above.
Togus Bash
STATISTICS
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Inferential Statistics
What does a negative correlation indicate?
A. No relationship.
B. A direct relationship.
C. An inverse relationship.
D. A strong relationship.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of a control group in an experiment?
A. To provide a baseline for comparison.
B. To manipulate the independent variable.
C. To increase sample size.
D. To ensure randomization.
Togus Bash
STATISTICS
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Inferential Statistics
In a regression equation, what does the intercept represent?
A. The predicted value when all predictors are zero.
B. The slope of the line.
C. The correlation coefficient.
D. The standard deviation.
Togus Bash
STATISTICS
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Inferential Statistics
What does it mean if a result is statistically significant?
A. The result is important.
B. The result is likely due to chance.
C. The result is unlikely due to chance.
D. The result is not important.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is a characteristic of a normal distribution?
A. Skewed to the right.
B. Symmetrical around the mean.
C. Mean is less than median.
D. All values are equal.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of a hypothesis test?
A. To prove a theory.
B. To determine if there is enough evidence to reject the null hypothesis.
C. To collect data.
D. To summarize data.
Togus Bash
STATISTICS
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Inferential Statistics
Which test would you use to compare the means of three or more groups?
A. t-test.
B. ANOVA.
C. Chi-square test.
D. Z-test.
Togus Bash
STATISTICS
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Inferential Statistics
What is the effect of increasing sample size on the standard error?
A. It increases.
B. It decreases.
C. It has no effect.
D. It doubles.
Togus Bash
STATISTICS
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Inferential Statistics
In a one-way ANOVA, what does the F-statistic compare?
A. Between-group variance to within-group variance.
B. Means of different groups.
C. Sample sizes of different groups.
D. Total variance to error variance.
Togus Bash
STATISTICS
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Inferential Statistics
What is the main focus of inferential statistics?
A. Describing data.
B. Making inferences about populations.
C. Collecting data.
D. Organizing data.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is an assumption of the t-test?
A. Samples are independent.
B. Populations are normally distributed.
C. Variances are equal.
D. All of the above.
Togus Bash
STATISTICS
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Inferential Statistics
What does a confidence level of 99% imply?
A. 1% chance of error.
B. 5% chance of error.
C. 95% chance of accuracy.
D. 99% chance of accuracy.
Togus Bash
STATISTICS
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Inferential Statistics
What is the main purpose of post-hoc tests in ANOVA?
A. To compare means of two groups.
B. To determine the overall significance.
C. To identify which specific groups differ.
D. To calculate effect size.
Togus Bash
STATISTICS
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Inferential Statistics
In regression analysis, what does R? represent?
A. The slope of the regression line.
B. The correlation coefficient.
C. The proportion of variance explained.
D. The intercept of the regression line.
Togus Bash
STATISTICS
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Inferential Statistics
What type of data is required for ANOVA?
A. Categorical data only.
B. Continuous data only.
C. Both categorical and continuous data.
D. Ordinal data only.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is true about a 95% confidence interval?
A. It guarantees that the population parameter is within the interval.
B. It means 95% of the data falls within the interval.
C. It means that 95% of the time the interval will contain the parameter.
D. It means that if we repeat the study, 95% of intervals will contain the parameter.
Togus Bash
STATISTICS
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Inferential Statistics
What is the null hypothesis in a t-test for means?
A. There is a difference between means.
B. There is no difference between means.
C. Means are equal.
D. Means are not equal.
Togus Bash
STATISTICS
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Inferential Statistics
In hypothesis testing, what does a (alpha) represent?
A. Sample size.
B. Significance level.
C. Population mean.
D. Type I error rate.
Togus Bash
STATISTICS
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Inferential Statistics
What is the main assumption of linear regression analysis?
A. Normality of residuals.
B. Homogeneity of variances.
C. Independence of observations.
D. All of the above.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is a non-parametric test?
A. t-test.
B. ANOVA.
C. Mann-Whitney U test.
D. Z-test.
Togus Bash
STATISTICS
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Inferential Statistics
What does the term "power" refer to in hypothesis testing?
A. Probability of rejecting a false null hypothesis.
B. Probability of accepting a true null hypothesis.
C. Probability of making a Type I error.
D. Probability of making a Type II error.
Togus Bash
STATISTICS
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Inferential Statistics
In which scenario would you use a chi-square test?
A. Comparing means of two groups.
B. Analyzing categorical data.
C. Testing correlation between two variables.
D. Estimating population parameters.
Togus Bash
STATISTICS
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Inferential Statistics
What is the formula for the standard error of the mean?
A. s/vn.
B. s*n.
C. n/s.
D. s?/n.
Togus Bash
STATISTICS
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Inferential Statistics
What does a Type I error represent?
A. Rejecting a true null hypothesis.
B. Accepting a false null hypothesis.
C. Rejecting a false null hypothesis.
D. Accepting a true null hypothesis.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following indicates a strong positive correlation?
A. 0.
B. 0.5.
C. 0.8.
D. -0.9.
Togus Bash
STATISTICS
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Inferential Statistics
What is the purpose of a confidence interval?
A. To estimate the mean of a sample.
B. To estimate the range of a population parameter.
C. To test a hypothesis.
D. To determine causation.
Togus Bash
STATISTICS
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Inferential Statistics
What does the Central Limit Theorem state?
A. Sample means will always be normal.
B. The distribution of sample means approaches normality as sample size increases.
C. All populations are normally distributed.
D. Large samples eliminate sampling error.
Togus Bash
STATISTICS
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Inferential Statistics
Which of the following is NOT a type of hypothesis test?
A. t-test.
B. ANOVA.
C. Regression analysis.
D. Chi-square test.
Togus Bash
STATISTICS
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Inferential Statistics
In a two-tailed test, what is the significance level typically used?
A. 0.01.
B. 0.05.
C. 0.1.
D. 0.15.
Togus Bash
STATISTICS
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Inferential Statistics
What does a p-value represent in hypothesis testing?
A. Probability of the null hypothesis being true.
B. Probability of obtaining the observed result.
C. Probability of making a Type I error.
D. Probability of making a Type II error.
? means here λ.