Statistics and Probability Exam

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Questions and Answers

Why is simple random sampling often preferred in statistical studies?

Every member of the population has an equal chance of being selected, reducing bias. (correct)
It ensures representation from specific subgroups within the population.
It is the only method that guarantees a sample perfectly mirroring the population.
It is the most cost-effective method for all types of populations.

How can a large standard deviation affect the interpretation of a dataset?

It guarantees the sample is representative of the population.
It suggests that the mean is not a reliable measure of central tendency. (correct)
It indicates that data points are clustered closely around the mean.
It always indicates errors in the data collection process.

In hypothesis testing, what does the p-value represent?

The probability of observing a test statistic as extreme as, or more extreme than, the one computed if the null hypothesis is true. (correct)
The probability that the null hypothesis is true.
The level of significance chosen before conducting the test.
The probability that the alternative hypothesis is false.

What is the primary purpose of calculating a z-score?

To normalize data, allowing comparison across different scales and distributions. (B) Signup and view all the answers

How does increasing the sample size generally affect the width of a confidence interval?

It narrows the confidence interval, increasing the precision of the estimate. (C) Signup and view all the answers

If a hypothesis test results in a p-value of 0.06, which of the following conclusions is most appropriate if using a significance level of 0.05?

Fail to reject the null hypothesis. (D) Signup and view all the answers

Which of the following is a key characteristic of a normal distribution?

The mean and median are approximately equal. (A) Signup and view all the answers

What does a sampling distribution represent?

The distribution of all possible values of a statistic calculated from samples of the same size drawn from a population. (C) Signup and view all the answers

What does the Central Limit Theorem state?

The sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population's distribution. (A) Signup and view all the answers

Which of the following factors affects the power of a statistical test the most?

The sample size and the effect size. (A) Signup and view all the answers

In the context of statistics, what is a parameter?

A fixed numerical value that describes a characteristic of a population. (C) Signup and view all the answers

What type of error occurs when you fail to reject a null hypothesis that is actually false?

Type II error (B) Signup and view all the answers

What is the role of percentiles in data analysis?

To indicate the value below which a given percentage of observations in a group of observations fall. (A) Signup and view all the answers

What is the purpose of stratification in stratified random sampling?

To ensure that each subgroup within the population is adequately represented in the sample. (B) Signup and view all the answers

In regression analysis, what does the R-squared value represent?

The proportion of variance in the dependent variable that is predictable from the independent variable(s). (C) Signup and view all the answers

Why is it important to check for outliers before conducting statistical analyses?

Outliers can disproportionately influence the results and lead to incorrect conclusions. (B) Signup and view all the answers

How does the t-distribution differ from the standard normal (z) distribution?

The t-distribution has heavier tails and is used when the population standard deviation is unknown and the sample size is small. (C) Signup and view all the answers

In time series analysis, what is the purpose of decomposition?

To break down a time series into its underlying components, such as trend, seasonality, and random noise. (A) Signup and view all the answers

What is the main reason for using non-parametric tests instead of parametric tests?

Non-parametric tests make fewer assumptions about the distribution of the data. (A) Signup and view all the answers

A researcher wants to determine if there is a significant difference in job satisfaction between employees working remotely and those working in the office. Which statistical test is most appropriate?

Independent samples t-test (A) Signup and view all the answers

Flashcards

Random Sampling

A method where every member of a population has an equal chance of being selected.

Parameter

A number that describes a characteristic of a population.

Statistic

A number that describes a characteristic of a sample.

Z-score

It tells you how many standard deviations from the mean your score is.

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Sampling Distribution

The distribution of a statistic obtained from all possible samples of a specific size taken from a population.

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Percentiles

Values that divide a data set into 100 equal parts.

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T-Table

A table used to find probabilities for a t-distribution.

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Study Notes

Statistics & Probability Exam Coverage encompasses several key topics from random sampling to percentiles
Exam types include multiple choice and problem solving