📊 statistics

1. مسئله را بیان می کنیم: می‌خواهیم بررسی کنیم آیا بین سه روش درمانی A، B و C در کاهش میزان افسردگی تفاوت معنی‌داری وجود دارد یا خیر در سطح معنی داری 5%. 2. داده‌ها به صورت زیر است

1. Statement: When the mean is computed for individual data, all values in the data set are used. Explanation: True. The mean (average) is found by summing all values and dividing

1. The problem is to understand the concept of a \textbf{statistical vector} in statistics and linear algebra. 2. A statistical vector often represents data points arranged as an o

1. Problem: A vaccine trial with 20 children, 15 developed immunity. (a) Probability at least 15 develop immunity. (b) Expected number and standard deviation.\n 1. (a) Let $X \sim

Problem statements: A pharmaceutical company tested a new vaccine on 20 children and 15 developed immunity; additional questions concern birth weights (normal), sample means (SBP),

1. **State the problem:** We are given scores of 20 students in Mathematics and Physics and asked to find the relationship using the Pearson product-moment correlation coefficient.

1. **Problem Statement:** Analyze monthly sales data for Tan Tan LTD using time series methods including 3-point moving averages, seasonal indices (multiplicative and additive), fo

1. The numbers given are 570, 300, 40, 130, 210, 200, 130, and 130. 2. Since the problem is not explicitly stated, a reasonable assumption is that we may be asked to analyze or sum

1. Problem statement: Represent the given data on a graph. 2. Note: you did not supply data, so I will illustrate the steps with an example dataset and show all intermediate work.

1. Find the range, standard deviation, and variance for the sample data: 3, 4, 6, 7, 12, 2, 1. 2. Find the standard deviation for the population data: 4, 9, 12, 16, 17, 20.

1. Problem statement. Andy believes that 76% of his customers are satisfied with the food quality, and a random sample of 84 customers is taken to estimate probabilities for counts

1. **Stating the problem:** Andy believes 72% of his customers are satisfied. From a sample of 92, we want probabilities of satisfaction numbers.

1. The problem asks us to analyze two graphs representing the number of graduates from a community college from 1999 to 2003 and to determine which graph is misleading and why. 2.

Problem: The masses of all of the Roman coins in a museum are recorded in the histogram below. 108 of the coins each weigh between 8 g and 17 g. Work out how many Roman coins are i

1. We are given 48 observations and need to create a frequency distribution, draw a histogram, and impose a frequency polygon. 2. First, arrange the data into class intervals. Let'

1. **Problem Statement:** Estimate the relationship between GPA and ACT scores with OLS regression for 8 students. 2. **Calculate means:**

1. **State the problem:** Given weekly wages distribution, draw the cumulative frequency curve and find deciles $D_7, D_8, D_3$ and percentiles 50th and 75th. 2. **Create cumulativ

1. The problem involves understanding the variance formula given by $$\operatorname{Var}(\bar{X}) = \sigma^2 \cdot \frac{n^2}{m n^2} = \sigma^2 \cdot \frac{1}{m}$$

1. Let's start by defining grouped data and ungrouped data. 2. Ungrouped data refers to data collected in raw form without any categorization. For example, the ages of 5 people: 21

1. Let's consider a problem involving mean (average): Find the mean of the data set $\{2, 4, 6, 8, 10\}$.

1. The problem asks about the concepts of census and sampling in various scenarios related to schools, factories, councils, manufacturers, and garages. 2. For question 1a, a census