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 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.
In a Chi-square test for independence, small expected frequencies can lead to a ________ Chi-square value.
- constant
- larger
- smaller
- zero
In a Chi-square test for independence, small expected frequencies can lead to a larger Chi-square value. This is because the Chi-square value is inflated by small expected frequencies, which can lead to a significant result even when there is no substantial relationship between the variables.
What does a 95% confidence interval estimate?
- The mean of the sample
- The range within which 95% of the data points lie
- The standard deviation of the population
- The true population parameter with a 95% level of confidence
A 95% confidence interval estimates the range within which we are 95% confident that the true population parameter lies. It is not about the range of the data or the mean of the sample.
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.
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.
_______ 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 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.
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 effect of monotonic transformations on Spearman’s rank correlation coefficient?
- They decrease the coefficient
- They don't affect the coefficient
- They increase the coefficient
- They make the coefficient negative
Monotonic transformations do not affect the Spearman’s rank correlation coefficient. This is because Spearman's correlation is based on the rank order of data, and monotonic transformations preserve this order.
In the context of cluster analysis, what is the 'centroid'?
- The average distance between clusters
- The geometric center of a cluster
- The largest point in a cluster
- The smallest point in a cluster
The centroid is the geometric center of a cluster. In other words, it's the mean value of all the points in a specific cluster.
_______ is a measure of how spread out the numbers in a dataset are around the mean.
- Median
- Range
- Standard Deviation
- Variance
Standard deviation is a measure of how spread out the numbers in a dataset are around the mean. It measures the average distance between each data point and the mean. The higher the standard deviation, the more spread out the data is.