📊 statistics

1. **Problem statement:** We have a frequency distribution of amounts spent by customers in intervals and their frequencies.

1. **Problem Statement:** We have a frequency distribution of interview durations and need to calculate the mean and standard deviation, then interpret them.

1. 问题陈述：使用独立样本进行统计分析时，通常是比较两个独立样本的均值或其他统计量。 2. 公式介绍：对于两个独立样本均值的比较，常用的t检验统计量公式为：

1. **Problem statement:** We want to find a 98% confidence interval for the mean difference in wing lengths between birds from northern and southern regions, and then interpret whe

1. **Problem Statement:** Construct a stem-and-leaf display for the given exam scores of 24 students: 56, 62, 68, 74, 71, 69, 85, 78, 81, 55, 60, 67, 72, 66, 59, 73, 88, 90, 47, 52

1. **State the problem:** We want to find a 95% confidence interval for the mean difference in wing lengths of birds between northern and southern regions, given sample data. 2. **

1. **State the problem:** We want to find a 90% confidence interval for the mean difference in wing lengths between birds from northern and southern regions, given sample statistic

1. **Stating the problem:** We want to understand the concept of unbiasedness in statistics and see examples. 2. **Definition:** An estimator \(\hat{\theta}\) of a parameter \(\the

1. The problem involves interpreting a line plot showing the "Amount of melted yellow wax" at three points: 0, 1/2, and 1. 2. Each point has a number of X's stacked vertically repr

1. The problem is to find the mean (average) of each data set. 2. The formula for the mean is:

1. **Problem Statement:** We are given a frequency polygon showing the number of goals scored by a football team in 25 matches. We need to complete a frequency table, find the mode

1. **State the problem:** We have a pie chart representing students' favorite sports with angles for Cricket (94°), Tennis (45°), and Football (x°). We need to find: (i) The value

1. **Problem Statement:** We have data on the amount of money 100 students spent on cellphone data in a week, grouped into class intervals with frequencies and midpoints. We need t

1. **State the problem:** We are given a grouped frequency distribution of marks and their frequencies. We need to calculate the mean mark of this distribution. 2. **Formula for me

1. The problem involves interpreting the p-value from a hypothesis test using the p-value method. 2. Given data: test statistic $z = 2.024$, p-value $= 0.043$, and the test is two-

1. **State the problem:** We want to test the claim that the population mean $\mu$ is different from 9 using a hypothesis test at the 0.05 significance level. 2. **Write the hypoth

1. **State the problem:** We want to test the claim that the population mean $\mu$ is different from 9 using a hypothesis test at the 0.05 significance level. 2. **Write the hypoth

1. **Problem Statement:** We have tip percentages for 450 meals and want to estimate the average tip percentage using random samples. 2. **Part A:** Given random IDs 16, 117, 307,

1. The problem asks to find the error in the sample mean computed in Part A and Part C, given the population mean $\mu = 12.58\%$ and sample means from Part A and Part C. 2. The er

1. **State the problem:** We are given 20 data points representing mean annual rainfall in millimeters and need to compute the sample variance. 2. **Formula for sample variance:**

1. **State the problem:** We want to analyze if the air contamination levels differ with distance from the factory complex and understand the relationship between distance and cont