📊 statistics

1. **State the problem:** We have data for number of absences $x$ and final grades $y$. We want to find the linear regression equation $\hat{y} = mx + b$ that predicts final grade

1. **State the problem:** We have a sample of 400 adults, with 180 believing their student loan debt is unmanageable. We want to find the degree of confidence for a confidence inte

1. The type of data personally collected is **primary data**. 2. The type of data involving numbers and quantities is **quantitative data**.

1. **بيان المشكلة:** نريد اختبار ما إذا كانت البيانات المشاهدة $O_i$ تختلف عن القيم المتوقعة $e_i$ باستخدام اختبار كاي-تربيع عند مستوى معنوية 0.05.

1. Problem (b): We want to find the sample size $n$ to estimate the percent defective within 2% with 95.45% confidence from a population of 4000. 2. Formula for sample size when es

1. **State the problem:** We want to find the p-value for a one-sample z-test for proportions where the null hypothesis is $H_0: p = 0.75$ and the alternative hypothesis is $H_a: p

1. **Problem Statement:** We have data on the number of car accidents per week over 80 weeks with frequencies for 0, 1, 2, and 3 accidents. We want to test if this data follows a P

1. The problem is to understand and use the formula for variance, which is given by $$\sigma^2 = \sum \left[(x - \mu)^2 \cdot p(x)\right]$$ where $\sigma^2$ is the variance, $x$ re

1. **State the problem:** Find the mean and variance of the data set: 39, 56, 120, 597, 965, 294, 565, 470, 1100, 1100, 281, 60, 216, 286, 890, 494, 2000, 857, 443, 515. 2. **Conve

1. **Problem Statement:** We want to find the sample size needed to estimate the percent defective in a population of 4000 items with a margin of error of 2% and a confidence level

1. مسئله: داده‌های نمونه‌ای از دو گروه با فشار باد زیاد و فشار باد استاندارد داریم که شامل اندازه نمونه ($n_1=14$, $n_2=15$)، میانگین‌ها ($\bar{X}_1=43$, $\bar{X}_2=\frac{40}{7} \a

1. مسئله: مقایسه دو گروه نمونه با اندازه‌های نمونه $n_1=14$ و $n_2=15$، میانگین‌های نمونه $\bar{X}_1=43$ و $\bar{X}_2=\frac{40}{7}$ و انحراف معیارهای نمونه $S_1=1$ و $S_2=\frac{1}{

1. مسئله را بیان می‌کنیم: می‌خواهیم تفاوت میانگین دو نمونه با اندازه‌های $n_1=14$ و $n_2=15$، میانگین‌های نمونه $\bar{X}_1=43$ و $\bar{X}_2=\frac{40}{7}$ و انحراف معیارهای نمونه $S

1. **Problem Statement:** Calculate the total sample size in a multistage stratified sampling design where two universities are selected, each with 16 colleges, and from each colle

1. **Problem Statement:** Given the data of student scores:

1. **State Bayes’ theorem:** Bayes’ theorem relates conditional probabilities and is stated as:

1. **Énoncé du problème :** Nous avons une série double (x, y) avec des classes d'ancienneté $x$ et des classes de salaire $y$.

1. **Stating the problem:** We want to perform an inferential statistical study to understand how students cope with stress based on the given bar graph data. 2. **Data summary:**

1. The problem involves analyzing voting preferences for five types of food: Italian, Mexican, Thai, Chinese, and Indian, based on rankings and number of ballots. 2. Each food type

1. **Problem statement:** Calculate the mean height, variance, and standard deviation for the heights of 8 students: 165, 170, 190, 180, 175, 185, 176, 184 cm.

1. The problem is to understand the difference between a quartile and a percentile. 2. Quartiles divide a data set into four equal parts, each containing 25% of the data. The three