📊 statistics

1. **Problem Statement:** Given advertising expenditure $X$ (in $100$ units) and sales revenue $Y$ (in $1000$ units) as: $X = [1, 2, 3, 4, 5]$

1. **State the problem:** We want to test if the violent crime rates differ significantly among the four cities: Toronto, St. Catharines, Hamilton, and Sudbury. 2. **Write the hypo

1. The problem is to understand the meaning and correct usage of $\bar{R}^2$ (R-bar squared) in statistics, particularly in regression analysis. 2. $\bar{R}^2$, or adjusted R-squar

1. **State the problem:** We are given a regression model with sample size $n=8$, $R^2=0.937$, and an ANOVA table. We need to find the adjusted $R^2$ (denoted $\bar{R}^2$) and the

1. **State the problem:** We are given a regression model with sample size $n=8$, $R^2=0.937$, and an ANOVA table. We need to find the adjusted $R^2$ (denoted $\bar{R}^2$) and the

1. **Problem Statement:** Given advertising expenditure $X$ (in $100$ units) and sales revenue $Y$ (in $1000$ units) as follows: $X: 1, 2, 3, 4, 5$

1. **Problem Statement:** Find the mean and variance of the sampling distribution of the mean given a population variance of 2 and a sample size of 169. Also, find the standard err

1. **Problem Statement:** Find the mean and variance of the sampling distribution of the mean. Given the population variance $\sigma^2 = 2$ and sample size $n = 169$, find the stan

1. The problem asks to determine the standard error of the estimate, denoted as $S_{YX}$. 2. The standard error of the estimate measures the average distance that the observed valu

1. The problem asks to interpret the meaning of $r^2$ (coefficient of determination) in the context of explaining variation between two variables. 2. The formula for $r^2$ is:

1. **Problem statement:** We are given the sum of squares due to regression (SSR) and the total sum of squares (SST) from a wine quality model. We need to find the coefficient of d

1. **Problem statement:** We have a normal random variable $X$ with mean $\mu = 30$ and unknown variance $\sigma^2$. Given that $P(X < 35) = 0.69$, we need to find the variance $\s

1. **Problem Statement:** An agronomist conducted an experiment to study the relationship between fertilizer amount and corn yield. We have data for fertilizer applied (independent

1. **Problem 1: Calculate Mean, Median, and Mode** Given the data set: 3, 7, 7, 2, 9, 10, 3, 7, find the mean, median, and mode.

1. **Problem Statement:** We are given 15 samples, each with 10 measurements of soft-drink fill volumes. We need to set up the $\bar{x}$ and $R$ charts, check for statistical contr

1. **Problem Statement:** We are given 15 samples of size $n=10$ with fill height deviations from the nominal fill height of soft-drink bottles. We need to:

1. **Problem Statement:** Calculate the arithmetic mean and geometric mean of pollutant concentrations 20, 30, 50, and 120 micrograms per cubic meter.

1. **Problem Statement:** Calculate the arithmetic mean and geometric mean of pollutant concentrations 20, 30, 50, and 120 micrograms per cubic meter, then determine which mean pro

1. **Problem statement:** We have a binomial random variable $X$ representing the number of cyclists using a mobile phone while cycling out of 40 randomly selected cyclists. The pa

1. **Problem Statement:** We are given reaction times (in milliseconds) of 30 participants and asked to construct a frequency distribution table with tally marks.

1. **Problem Statement:** We are given reaction times (in milliseconds) of 30 participants and asked to construct a frequency distribution table.