1. Define the following terms:
a. Population: The entire group of individuals or items being studied.
b. Sample: A subset of the population selected for study.
c. Parameter: A numerical value that describes a population characteristic.
d. Statistic: A numerical value that describes a sample characteristic.
2. Explain the difference between inferential statistics and descriptive statistics.
- Descriptive statistics involve describing, summarizing, and organizing data, while inferential statistics involve making predictions, inferences, and decisions about the population based on the sample data.
3. What is the purpose of hypothesis testing in statistics?
- Hypothesis testing is used to determine whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis.
4. Define Type I error and Type II error in hypothesis testing.
- Type I error occurs when the null hypothesis is rejected when it is true.
- Type II error occurs when the null hypothesis is not rejected when it is false.
5. What is the difference between a one-tailed test and a two-tailed test?
- In a one-tailed test, the alternative hypothesis is directional (e.g., greater than or less than a certain value), while in a two-tailed test, the alternative hypothesis is non-directional (e.g., not equal to a certain value).
6. Calculate the mean, median, and mode for the following data set: 2, 4, 6, 8, 10.
- Mean: (2+4+6+8+10)/5 = 6
- Median: 6 is the middle value
- Mode: There is no mode in this data set
7. What is the standard deviation and how is it calculated?
- The standard deviation is a measure of the dispersion or variability of a set of values. It is calculated by taking the square root of the variance.
8. Explain the difference between correlation and regression in statistics.
- Correlation measures the strength and direction of a relationship between two variables, while regression predicts the value of one variable based on the value of another variable.
9. What is the difference between a random sample and a convenience sample?
- A random sample is selected in a way that every member of the population has an equal chance of being included, while a convenience sample is selected based on what is most convenient or readily available.
10. Give an example of a situation in which you would use a chi-square test in statistics.
- A chi-square test can be used to determine if there is a relationship between two categorical variables, such as testing whether gender is related to political party affiliation.
Math Statistics unit test 7
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