📊 statistics

1. **Stating the problem:** We have marks and their corresponding weights for five subjects. We want to calculate the weighted mean of the marks and compare it to the simple mean.

1. **Problem Statement:** We have monthly incomes (in thousands of BDT) of 9 employees: 22, 25, 27, 24, 30, 21, 100, 23, 26. We need to find the mean and median income and determin

1. **Problem statement:** We want to find the areas under the standard normal distribution curve for the following cases: (a) Between $z=0$ and $z=1.77$

1. **Stating the problem:** We have typing speeds (words per minute) from four word processors (A, B, C, D), with multiple measurements each. We want to test if the observed differ

1. **State the problem:** We want to find the Pearson product-moment correlation coefficient $r$ between the years of higher education (variable $X$) and monthly salary in thousand

1. **Problem (d): Compute the 95% confidence interval for $\beta_1$** To compute the confidence interval for $\beta_1$, we use the formula:

1. **State the problem:** We have typing speed data from four word processors A, B, C, D. We want to test if the differences in their mean typing speeds are statistically significa

1. **State the problem:** We want to test if there is a significant difference among the means of typing speeds (words per minute) of four different word processors (A, B, C, D). 2

1. The problem asks for t-tests for four groups labeled a, b, c, and d. 2. A t-test compares means of two groups to see if they are significantly different.

1. **Stating the problem:** We have four word processors (A, B, C, and D) with observations of words typed per minute. We want to test if the differences among the means of these f

1. **Problem 1: 90% Confidence Interval for Mean Annual Income** Given:

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