📊 statistics

1. **Problem statement:** We have a dataset with variables $x$ and $y$. We want to fit both a linear model and a quadratic model to the data, then calculate the difference between

1. **Problem statement:** We have a normally distributed variable $X$ with mean $\mu = 30$ and standard deviation $\sigma = 4$. We want to find probabilities for different ranges o

1. **Problem statement:** We have a sample of growing stock volumes (in m^3/ha) from randomly arranged sample plots: 803, 682, 347, 808, 664, 472, 613, 199, 403, 564, 267, 396. We

1. **State the problem:** We have a sample of growing stock volumes (in m^3/ha) from randomly arranged sample plots: -803, -682, -347, -808, -664, -472, -613, -199, -403, -564, -26

1. **State the problem:** We have a sample of growing stock volumes (in m^3/ha) from randomly arranged sample plots: -803, -682, -347, -808, -664, -472, -613, -199, -403, -564, -26

1. **Problem Statement:** We need to perform three linear regressions using the dataset of countries with variables: Surface Area (independent variable), Population, and Sex Ratio

1. **State the problem:** We want to determine who performed better relative to their class by comparing Lisa's and Kevin's scores using z-scores. 2. **Formula for z-score:**

1. The problem asks to find the values of $z_1$ and $z_2$ such that the area under the standard normal curve between $z_1$ and $z_2$ is 0.8812. 2. The standard normal distribution

1. The problem asks for the area under the standard normal curve to the left of $z=1.42$. This area represents the cumulative probability $P(Z \leq 1.42)$ where $Z$ is a standard n

1. The problem asks for the probability that a standard normal variable $Z$ lies between $-2.85$ and $1.74$, i.e., $P(-2.85 < Z < 1.74)$. 2. For a standard normal distribution, pro

1. The problem asks to find the value of $k$ such that the area to the right of $k$ under the standard normal distribution curve is $P(z>k) = 0.9991$. 2. This means we want to find

1. The problem asks for the area under the standard normal curve to the right of $z = -2.34$. 2. The standard normal distribution is symmetric about zero, and the total area under

1. **State the problem:** We have a sample data set: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55. We want to find the new standard deviation if every observation is multiplied by 3.

1. **State the problem:** We need to find the variance of the ages of 16 employees given the data: 22, 58, 25, 35, 35, 40, 40, 35, 43, 53, 47, 22, 53, 35, 58, 25. 2. **Formula for

1. The problem is to find the formula for the median in grouped data. 2. The median is the value that divides the data into two equal halves.

1. The problem is to find the formula for the median of grouped data. 2. The median is the value that divides the data into two equal halves.

1. **State the problem:** We are given a standard normal distribution with a shaded area representing the probability 0.2881 between 0 and $h$. We need to find:

1. **State the problem:** We have a normal distribution for replacement times with mean $\mu = 12.6$ years and standard deviation $\sigma = 1.5$ years.

1. Mann-Whitney U Test: - Purpose: To compare differences between two independent samples when data is not normally distributed.

1. **Mann-Whitney U Test** - This test compares differences between two independent groups when the dependent variable is either ordinal or continuous but not normally distributed.

1. **Problem Statement:** Construct a frequency distribution table (FDT) for the given student scores using a class interval of 6, starting with the lowest value as the lowest lowe