📊 statistics

1. The problem asks which measures of position divide a distribution into 100 equal parts. 2. Measures of position are values that divide a data set into equal parts.

1. Stating the problem: Given a frequency distribution with class intervals and frequencies \(7, p, 10, 9, 13\), find \(p\) if the mean is 54. 2. Assign midpoints to each class int

1. Let's restate the problem: We need to perform hypothesis testing as asked in part bi) with more detailed explanation of the steps. 2. Define the null hypothesis ($H_0$) and the

1. **Problem Statement:** We are given the average age of year two students at MUBS as 23 years. A sample of 81 students shows an average age of 22 with variance 1. We are to under

1. **State the problem:** We are given a population mean $\mu=27$ and standard deviation $\sigma=5$, and we want to find the z-score for the data point 18. 2. **Recall the formula

1. **State the problem:** Given population mean $\mu = 165$, z-score $z = -1.84$, and data value $x = 218$, find the standard deviation $\sigma$. 2. **Recall the z-score formula:**

1. The problem asks us to identify which scenario matches the null hypothesis $p \geq 0.44$ and the alternative hypothesis $p < 0.44$. 2. The null hypothesis $p \geq 0.44$ means th

1. The problem provides a hypothesis test with null hypothesis $H_0: X \geq 6.4$ and alternative hypothesis $H_a: X < 6.4$. 2. This is a left-tailed test since $H_a$ involves less

1. The null hypothesis, denoted as $H_0$, typically states the status quo or a statement of no effect. Here, it is given as $p \leq 0.61$. 2. The alternative hypothesis, denoted as

1. **State the problem:** Jack wants to test if the true mean pH of river water is $7.4$ using a sample of size $28$, with population standard deviation $\sigma=0.29$ and significa

1. **State the problem:** Dmitry suspects the true proportion of odd numbers rolled is different from 0.5. 2. **Define hypotheses:**

1. Problem 1: Draw a histogram from the frequency distribution given for scores 5-40. 2. The score intervals are: 5-10, 10-15, 15-20, 20-25, 25-30, 30-35, 35-40.

1. **Problem Statement**: We have Physics and Chemistry marks of 8 students and want to analyze the relation with regression and correlation. 2. **Data**:

1. **Stating the problem:** We have two unbiased estimators \( l_1 \) and \( l_2 \) for the mean \( \theta = 0 \) of a distribution, and we need to determine which estimator is bet

1. The theory of estimation in statistics is about making inferences about population parameters based on sample data. 2. Key concepts include point estimation (estimating a parame

1. The problem is to plot the standard normal distribution curve, which is given by the probability density function $$y=\frac{1}{\sqrt{2\pi}}e^{-\frac{z^2}{2}}$$ and to find the a

1. The problem is to find the area under the standard normal curve from Z=0 to Z=1.35. 2. Using the table, split 1.35 into 1.3 (row) and 0.05 (column).

1. The problem asks us to find the area under the standard normal curve for various Z-value ranges. 2. We use the provided Z-table, where each entry represents the area from the me

1. Stating the problem: We are given daily high temperatures for 20 days and asked to construct a frequency distribution with class intervals of size 10. 2. Finding the range of th

1. **State the problem:** A nutritionist claims the new protein supplement increases average muscle mass gain compared to the standard supplement, whose mean gain is $\mu_0=3.0$ kg

1. **Problem Statement:** Given the age distribution of patients admitted to a hospital and their frequencies, find the mode and mean and then compare these measures of central ten