Intro to Statistics Final Exam | Latest Update | 2024/2025 | Graded A+
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Intro to Statistics Final Exam | Latest
Update | 2024/2025 | Graded A+
What is the main purpose of hypothesis testing in statistics?
To determine if there is enough evidence to reject a null hypothesis in favor of an alternative
hypothesis.
How does the concept of p-value help in making...
Intro to Statistics Final Exam | Latest
Update | 2024/2025 | Graded A+
What is the main purpose of hypothesis testing in statistics?
✔✔ To determine if there is enough evidence to reject a null hypothesis in favor of an alternative
hypothesis.
How does the concept of p-value help in making decisions about hypotheses?
✔✔ The p-value indicates the probability of obtaining test results at least as extreme as the ones
observed, assuming the null hypothesis is true.
Explain the difference between a population and a sample in statistical terms.
✔✔ A population includes all members of a specified group, while a sample is a subset of the
population used to make inferences about the population.
What is a confidence interval, and what does it represent in statistical analysis?
1
,✔✔ A confidence interval is a range of values derived from a data sample that is likely to
contain the value of an unknown population parameter. It provides an estimate with a certain
level of confidence.
Describe the Central Limit Theorem and its significance in statistics.
✔✔ The Central Limit Theorem states that the distribution of sample means approaches a normal
distribution as the sample size becomes large, regardless of the population's distribution. This
theorem is crucial because it allows for the use of normal probability theory for inference even
when the underlying population distribution is not normal.
What is the role of regression analysis in statistics?
✔✔ Regression analysis helps in understanding the relationship between dependent and
independent variables and predicting the value of the dependent variable based on the values of
the independent variables.
Define the term 'standard deviation' and explain its importance in data analysis.
2
,✔✔ Standard deviation measures the amount of variation or dispersion in a set of values. It is
important because it provides insight into the spread of the data and helps assess the consistency
or variability of the data.
What is the purpose of a chi-square test, and what types of data is it used for?
✔✔ A chi-square test assesses the association between categorical variables by comparing
observed frequencies with expected frequencies. It is used for data that is organized into
categories or groups.
Population ✔✔a collection of persons, things, or objects under study.
Sample ✔✔selecting a portion (or subset) of the larger portion
Parameter ✔✔A numerical characteristic of the whole population that can be estimated by a
statistic.
Ex: we consider all math classes to be the population, so the average number of points earned per
student over all math classes is a parameter.
3
, Statistic ✔✔A number that represents a property of the sample.
Ex: if we consider one math class to be the sample of the population of all the math classes, then
the average number of points earned by a student in that one math class at the end of the term is
an example of a statistic.
Variable ✔✔usually letters x and y, is a characteristic or measurement that can be determined for
each number of the population
Numerical variable: takes on a value with equal units such as weights in pounds and time in
hours.
Categorical variable: place the person or thing into a category (ex: party affiliation, gender, gpa).
Data ✔✔the actual values of the variable
What are the levels of measurement? ✔✔Nominal: no numerical value or order (names, labels,
categories)
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