📊 statistics

1. **State the problem:** Calculate the correlation coefficient $r_{x1y}$ using the formula: $$r_{x1y} = \frac{N \sum X_1Y - (\sum X_1)(\sum Y)}{\sqrt{[N \sum X_1^2 - (\sum X_1)^2]

1. The problem is to understand the null hypothesis $H_0$ and the alternative hypothesis $H_1$ in hypothesis testing. 2. The null hypothesis $H_0$ is a statement that there is no e

1. The problem is to understand what variance is in statistics. 2. Variance measures how much a set of numbers is spread out from their average (mean).

1. The problem is to understand the hazard function in a Cox proportional hazards model, given by: $$\lambda(t|X,\beta) = \lambda_0(t) \exp(X' \beta)$$

1. **Problem Statement:** We have two parts: (a) a binomial probability problem about attendance at a stadium where 70% are males, and (b) a normal distribution problem about meals

1. **Stating the problem:** We are given two sets of data points (X and Y) with some missing values represented by dots. We need to analyze the data by filling in the missing value

1. **State the problem:** We are given a frequency distribution with a missing frequency and the mean of the data is 22. We need to find the missing frequency. 2. **Given data:**

1. **Stating the problem:** We are given three groups with sample sizes $n_1=4$, $n_2=5$, $n_3=4$ and variances $s_1^2=6.67$, $s_2^2=2.50$, $s_3^2=6.67$. We want to test the homoge

1. **State the problem:** We are given three sets of data and need to calculate the mean ($\bar{x}$), the sum of squared differences from the mean ($\sum (x_i - \bar{x})^2$), and t

1. **Problem Statement:** We have 10 samples, each with 4 measurements, and a target process mean of 25. We need to:

1. The problem asks about predicting goals and which teams will score in a match. 2. This is not a straightforward math problem but involves probability and statistics, often model

1. The problem is to arrange a list of football match predictions from the safest to the worst. 2. To do this mathematically, we need a measure of "safety" or confidence for each p

1. **Problem statement:** We have a normally distributed random variable $X$ with mean $\mu = 10$ and standard deviation $\sigma = 2$.

1. The problem asks us to state the null hypothesis for testing the claim that 9 out of 10 doctors recommend aspirin, i.e., the population proportion $p=0.9$. 2. The null hypothesi

1. **Problem Statement:** Understand the formulas for Arithmetic Mean (AM) and Weighted Arithmetic Mean (WAM) and solve related problems. 2. **Formulas:**

1. The problem asks: What is the process of gathering and measuring information on targeted variables in an established system, which then enables one to answer relevant questions

1. **Stating the problem:** We have values of $X = 13, 18, 23, 28, 33, 38, 43, 48$ and their corresponding frequencies $f = 1, 2, 5, 11, 12, 11, 5, 1$. We need to find: - $f x$

1. **Stating the problem:** We are given a grouped frequency distribution and need to find the 30th percentile class and related values.

1. **Problem Statement:** We are given ungrouped data and want to find the $k^{th}$ percentile using the formula $$P_k = \frac{kN}{100}$$ where $N$ is the sample size and $k$ is th

1. **Problem Statement:** We have two classes with their test scores:

1. **Problem Statement:** Calculate Spearman's rank correlation coefficient for the given ranks of seven students in Statistics and Economics. 2. **Formula:** Spearman's rank corre