📊 statistics

1. **State the problem:** You have 20 possible questions, and the instructor will randomly pick 4 for the exam. You prepared exactly 4 questions. We want to find the probability th

1. **State the problem:** We need to find the critical value for a 95% confidence interval for the population mean nitrate concentration based on a sample of size 28. 2. **Identify

1. **State the problem:** We want to test if the doors are too short, i.e., if the mean height is less than 2058.0 mm. 2. **Set up hypotheses:**

1. **Problem Statement:** An economist wants to estimate the mean number of school children (in thousands) who read above their grade level in a major city in Florida. A sample of

1. The problem involves interpreting the meaning of a 99% confidence level in hypothesis testing. 2. A 99% confidence level means that if we were to repeat the experiment many time

1. **State the problem:** We want to calculate a 99% confidence interval for the mean sodium content in Oriental Spice Sauce based on a sample of 40 packages. 2. **Formula for conf

1. The problem involves understanding frequency (f) and relative frequency (fr) in two tables: one for clubs and one for games. 2. Frequency (f) is the count of occurrences, and re

1. **Stating the problem:** We are comparing two dot plots representing sprint times (in seconds) for the U.S. qualifier and the Olympic final. Lower times mean faster sprints. 2.

1. **State the problem:** We have a scatter plot showing the relationship between time spent studying (x) and quiz scores (y). We want to find the line of best fit (a linear equati

1. **State the problem:** We are given a frequency distribution with values $x = 4, 5, 6, 7, 8, 9$ and their corresponding frequencies $f = 10, 9, 14, 11, 5, 8$. We need to find th

1. **State the problem:** We are performing two one-way ANOVA tests to determine if there are significant differences among group means for two different scenarios: disordered thou

1. **State the problem:** Find the median of the data set: $-28, -28, -23, -12, -2, 8, -16, 14, 6, -3, -16, -24$. 2. **Recall the definition of median:** The median is the middle v

1. **State the problem:** We are given the number of touchdowns Luis scored in football games and the frequency of each number of touchdowns. We need to create a probability distri

1. **Problem Statement:** We have two problems involving paired data and linear regression.

1. The problem asks to explain Type I and Type II errors in hypothesis testing. 2. A Type I error occurs when we reject the null hypothesis $H_0$ even though it is true. It is a fa

1. **Job Search Problem:** Test the claim that the majority of employees are searching for new jobs using a 0.01 significance level. - Given: Sample size $n=195600$, sample proport

1. **Problem:** Determine if there is sufficient evidence of a linear correlation between casino size and revenue, and whether increasing size can increase revenue. 2. **Given Data

1. **Stating the problem:** We have actual sales and two forecast methods (M1 and M2) for 6 days. We need to calculate: - MAD (Mean Absolute Deviation) for M1 and M2

1. **State the problem:** Find the interquartile range (IQR) of the data set: 2, 8, 10, 12, 12, 14, 19, 23, 26, 31, 33. 2. **Recall the formula:** The interquartile range is given

1. **بيان المسألة:** نريد حساب الانحراف المعياري عن المتوسط الحسابي لأطوال 100 طالب موزعة حسب التكرار والفئات الطولية المعطاة.

1. **Problem Statement:** Find the quartiles $Q_1$, $Q_2$, $Q_3$ and deciles $D_1$, $D_3$ for the wages of 65 employees at the R and B company given the grouped frequency distribut