📊 statistics

1. **Problem Statement:** We have 52 annual maximum flow data points (in m^3/s) from the Colorado River at Black Canyon. We need to:

1. **State the problem:** Find the sample variance for the data set $\{2,4,6,8\}$. 2. **Formula for sample variance:**

1. **Step in computing variance and standard deviation using Excel for ungrouped data:** - Suppose your data is in cells A1 to A10.

1. The problem is to understand how to compute variance and standard deviation using Excel for ungrouped data, and also to understand Z tests, variance, standard deviation, and mea

1. The problem asks: What is a z test and when do we use it? 2. A z test is a statistical test used to determine if there is a significant difference between sample and population

1. **Problem Statement:** Calculate the following from the given population data:

1. Problem: Find the sample size for 275 BAM students with a margin of error of 1%. 2. Formula: Sample size $n = N \times E^2 / ((N-1) \times E^2 + Z^2)$ where $N$ is population si

1. **Problem Statement:** Professor Linda wants to determine the sample size for a population of 275 BAM students with a margin of error of 1%. 2. **Formula Used:** The sample size

1. The problem asks: How many customers queued for more than 20 minutes? 2. From the cumulative frequency graph, find the total number of customers who queued up to 20 minutes. The

1. **State the problem:** We want to test if the mean appreciation rate of houses in Sun Beach ($\mu_1$) is higher than that in North Arden ($\mu_2$) at a significance level $\alph

1. **Problem 47:** Given that $P(T_{18} > t) = 0.975$, find $t$. 2. The t-distribution with 18 degrees of freedom is symmetric and centered at zero.

1. The problem is to understand how to collect, organize, and interpret data effectively to answer specific questions. 2. The key idea is that data must be collected with a clear p

1. **Problem Statement:** We are testing if the difference in tranquilizer dosage (1.0 mg vs 1.5 mg) affects the time it takes rats to fall asleep using an independent samples t-te

1. **Problem Statement:** Test if the difference in tranquilizer dosage (1.0 mg vs 1.5 mg) affects the time to fall asleep using a t-test for independent samples at significance le

1. The problem asks us to find the interval containing the median pre-test score from the histogram data. 2. The median is the middle value when all scores are arranged in order. S

1. The problem is to find the moments of a function or distribution, which are measures of its shape and spread. 2. The $n$th moment about the origin is defined as $$\mu'_n = E[X^n

1. **Problem Statement:** Find the median of the observations arranged in ascending order: 11, 12, 14, 18, x+2, x+4, 30, 32, 35, 41. Given that the median is 24, find the value of

1. **Problem Statement:** Represent the given data using (a) Histogram, (b) Frequency polygon, (c) Frequency curve, and (d) Cumulative frequency curve (ogive). Given data:

1. **Stating the problem:** We have data on the number of gender equality training sessions attended ($x$) and the corresponding gender equality attitude scores ($y$) for six emplo

1. **Problem:** Find the mean of the given frequency distribution using (a) Direct method and (b) Assumed mean method with assumed mean 25. | Marks | 0-10 | 10-20 | 20-30 | 3

1. **Problem Statement:** We have a population with mean $\mu=140$ and standard deviation $\sigma=30$. We take a random sample of size $n=75$. We want to find probabilities related