The Central Limit Theorem states that the sampling distribution of the sample means approaches a ________ distribution as the sample size gets larger, regardless of the shape of the population distribution.
- Poisson
- binomial
- normal
- uniform
The Central Limit Theorem is a fundamental theorem in statistics that states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger, no matter what the shape of the population distribution. This outcome is significant because it enables us to make statistical inferences about the population mean based on the distribution of sample means.
What is the purpose of hypothesis testing in statistics?
- To compare the sample mean to the population mean
- To make inferences about a population based on sample data
- To understand the distribution of the data
- To visualize the data
Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. It's an inferential statistic that allows us to infer if our observed results deviate from null hypothesis by chance or by a true statistical difference.
The p-value in a hypothesis test is the probability of getting a sample statistic as extreme as the test statistic, given that the _______ hypothesis is true.
- Alternative
- Null
- Original
- Random
In the context of hypothesis testing, the p-value is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true.
What are the assumptions required for a distribution to be considered a Poisson distribution?
- The events are dependent on each other
- The events are occurring at a constant mean rate and independently of the time since the last event
- The events have more than two possible outcomes
- The number of trials is fixed
The key assumptions for a Poisson distribution are that the events are happening at a constant mean rate and independently of the time since the last event. This is often used for modeling the number of times an event occurs in a given interval of time or space.
What is the relationship between the mean and the standard deviation in a normal distribution?
- The mean is always larger than the standard deviation
- The mean is the midpoint of the distribution, and the standard deviation measures the spread
- The standard deviation is always larger than the mean
- There is no relationship between the mean and the standard deviation
In a normal distribution, the mean is the center of the distribution and represents the "average" value. The standard deviation measures the dispersion around the mean. Roughly 68% of the data falls within one standard deviation of the mean in a normal distribution.
The conditional probability of A given B is denoted as ________.
- P(A + B)
- P(A / B)
- P(A B)
- P(A ∩ B)
The conditional probability of A given B is denoted as P(A
What is the primary goal of random sampling?
- To always select the same individuals
- To ensure that every member of the population has an equal chance of being selected
- To select individuals who are likely to give the desired results
- To select the individuals who are easiest to reach
The primary goal of random sampling is to ensure that every member of the population has an equal chance of being selected. This helps to reduce bias and increase the likelihood that the sample is representative of the population, which makes the results more valid and generalizable.
_______ regression is a method used to handle multicollinearity by adding a degree of bias to the regression estimates.
- Logistic
- Polynomial
- Ridge
- Simple linear
Ridge regression handles multicollinearity by introducing a degree of bias to the regression estimates, reducing their variance, and making them more reliable.
What are the assumptions made by the Spearman’s Rank Correlation test?
- The data is continuous and the relationship is monotonic
- The data is normally distributed and linear
- The data is ordinal and the relationship is linear
- The data is ordinal or continuous and the relationship is monotonic
The Spearman’s Rank Correlation test assumes that the variables are ordinal or continuous and that the relationship between them is monotonic. It does not require the relationship to be linear or the data to be normally distributed.
What are the limitations of using mean as a measure of central tendency?
- It can't be used with large data sets
- It can't be used with small data sets
- It is difficult to calculate
- It is highly sensitive to outliers
The main limitation of the mean as a measure of central tendency is that it is highly sensitive to outliers or extreme values. An outlier can skew the mean and make it a less accurate representation of the data. Moreover, mean does not describe the middle value or most common value in the dataset, which are often important characteristics.