📊 statistics

1. **Problem Statement:** Determine if there is a statistically significant relationship between students' travel time (in minutes) and their midterm exam scores at a 0.05 signific

1. **Stating the problem:** We have two data sets: midterm scores and travel times. We want to analyze the first data set, the midterm scores. 2. **Formula and rules:** To analyze

1. **Problem Statement:** Determine if there is a statistically significant relationship between students' travel time (independent variable $x$) and their midterm exam scores (dep

1. **Problem:** Find the area below $x=36$ for a normal distribution with mean $\mu=27$ and standard deviation $\sigma=14$. 2. **Formula:** Use the standard normal variable $Z=\fra

1. **Problem Statement:** Given a frequency distribution with class intervals and frequencies, find the First Quartile (Q1), Third Quartile (Q3), 5th Decile (D5), 9th Decile (D9),

1. **State the problem:** We want to find the probability that a randomly selected technician's salary is greater than 80000 given the average salary is 82450. 2. **Identify the di

1. **بيان المشكلة:** نريد اختبار ما إذا كانت البيانات التي تم جمعها عن عدد المستهلكين في 42 مركز تسويق تتبع توزيع ذي الحدين مع احتمال نجاح $p=0.2$ عند مستوى معنوية $\alpha=0.05$.

1. **بيان المسألة:** لدينا بيانات عن عدد المتسوّقين في 42 مركز تسويق وعدد الأسواق التي تحقق كل عدد متسوّقين. نريد اختبار ما إذا كانت هذه البيانات تتوافق مع توزيع ذي الحدين Binomial

1. **بيان المسألة:** لدينا بيانات عن عدد المتسوقين في 42 مركز تسويق وعدد الأسواق التي بها هذا العدد من المتسوقين.

1. **Problem Statement:** We have a class of 20 students, each recording the number of coins in their pockets. The data is given as:

1. **بيان المشكلة:** نريد اختبار ما إذا كانت البيانات المعطاة تتوافق مع توزيع ذي الحدين Binomial distribution عند مستوى معنوية 0.05، مع معرفة أن $p=0.2$.

1. **بيان المشكلة:** نريد اختبار ما إذا كانت البيانات المعطاة تتوافق مع توزيع ذي الحدين Binomial distribution عند مستوى معنوية 0.05.

1. **Problem Statement:** Predict the final grade for a student who misses five days using the least-squares regression line.

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