Confidence Intervals

Introduction to Confidence Intervals A Confidence Interval (CI) is a range of values, derived from a sample, that is likely to contain the value of an unknown population parameter. The key idea behind confidence intervals is to provide an estimated…

Hypothesis Testing

Introduction to Hypothesis Testing Hypothesis testing is a fundamental statistical method used to determine whether there is enough evidence to reject a null hypothesis ($H_0$) in favor of an alternative hypothesis ($H_1$). It is commonly used in various fields like…

Introduction to Statistical Inference I: Classical Methods

Statistical inference helps us make decisions or predictions about a population based on sample data. In classical methods of inference, we focus on point estimation, interval estimation, hypothesis testing, and linear regression. These are the cornerstones of applied statistics, frequently…

Statistical Inference Classical Methods

A Comprehensive Guide to Statistical Inference: Classical Methods Statistical Inference is a fundamental area in statistics, where conclusions are drawn about a population based on a sample of data. The goal is to make educated guesses or inferences about the…

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 408 gram setting. It is believed that the machine is overfilling the bags. A 13 bag sample had a mean of 416 grams with a variance of 169. Assume the population is normally distributed. Is there sufficient evidence at the 0.01 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 408 $The Sample Mean $ (\bar{x}) = 416 $The Sample Variance $ (s^2) = 169 $The Sample Size $ (n) = 13 $ $\therefore$ The Sample Standard Deviation $ (s) = \sqrt{169} = 13…

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is overfilling the bags. A 14 bag sample had a mean of 415 grams with a variance of 144. Assume the population is normally distributed. Is there sufficient evidence at the 0.02 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 409 $The Sample Mean $ (\bar{x}) = 415 $The Sample Variance $ (s^2) = 144 $The Sample Size $ (n) = 14 $ $\therefore$ The Sample Standard Deviation $ (s) = \sqrt{144} = 12…

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 412 gram setting. It is believed that the machine is overfilling the bags. A 8 bag sample had a mean of 419 grams with a variance of 169. Assume the population is normally distributed. Is there sufficient evidence at the 0.02 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 412 $The Sample Mean $ (\bar{x}) = 419 $The Sample Variance $ (s^2) = 169 $The Sample Size $ (n) = 8 $ $\therefore$ The Sample Standard Deviation $ (s) = \sqrt{169} = 13…

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 407 gram setting. It is believed that the machine is overfilling the bags. A 11 bag sample had a mean of 414 grams with a variance of 144. Assume the population is normally distributed. Is there sufficient evidence at the 0.05 level that the bags are overfilled?

Answer:Given:The Hypothesized Mean $ (\mu) = 407 $The Sample Mean $ (\bar{x}) = 414 $The Sample Variance $ (s^2) = 144 $The Sample Size $ (n) = 11 $ $\therefore$ The Sample Standard Deviation $ (s) = \sqrt{144} = 12…