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gxc9800
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The probability ##22c8 ( (0.6)^8 )( (0.4)^14)## is the likelihood of drawing exactly this sample assuming the claim is true. When testing the hypothesis, you are comparing the cumulative probability of this sample (at least 8 people), against the claim.gxc9800 said:
Population variance is a measure of how spread out a population's data is from its mean. It is important to test because it allows us to understand the variability within a population and make comparisons between different populations.
The formula for testing population variance is (Σ(xi - μ)^2)/N, where Σ is the sum of the squared differences between each data point (xi) and the population mean (μ), and N is the number of data points in the population.
The results of a test for population variance are typically presented as a single number, known as the variance. A larger variance indicates a greater spread of data points from the mean, while a smaller variance indicates a more tightly clustered set of data points.
Some common methods for testing population variance include the Chi-Square test, the F-test, and the Levene's test. These tests involve calculating the variance of the population and comparing it to a critical value to determine if there is a significant difference between populations.
One limitation of testing population variance is that it assumes the data is normally distributed, which may not always be the case. Additionally, it can be affected by outliers in the data, and may not accurately capture the variability in a population if the sample size is too small.
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