📊 statistics

1. The problem is to recalculate the test statistic correctly when the previous calculation was wrong. 2. The test statistic formula depends on the type of test (e.g., z-test, t-te

1. **State the problem:** We are testing the claim about the population variance $\sigma^2$ with the hypotheses: $$H_0: \sigma^2 = 30.9$$

1. The problem asks to identify the trend shown by a scatter plot. 2. A scatter plot shows a positive trend if the points generally rise from the lower-left to the upper-right.

1. The problem asks to determine the trend shown by a scatter plot where points generally decrease as $x$ increases. 2. A positive trend means $y$ increases as $x$ increases.

1. The problem asks to determine if the scatter plot shows a positive trend, a negative trend, or no trend. 2. A positive trend means as $x$ increases, $y$ tends to increase.

1. The problem asks us to identify the trend shown by a scatter plot with points spread in the center of the graph. 2. A positive trend means points generally go upward from left t

1. **State the problem:** We want to find the binomial probability $P(X=20)$ where $n=42$ trials, probability of success $p=0.5$, and $X$ is the number of successes.

1. **State the problem:** We are given the number of pieces in each puzzle and their frequencies: 20 pieces (2 puzzles), 30 pieces (1 puzzle), 50 pieces (3 puzzles), 80 pieces (1 p

1. **State the problem:** We want to estimate how many applicants in the 2026 DiscoverEU round have postal codes starting with the digit "2".

1. **State the problem:** Maya wants to describe typical home values in her neighborhood using statistics that are not greatly affected by extreme values (outliers). 2. **Important

1. The problem asks to predict the relationship between the mean and median beverage prices based on the shape of the graph. 2. The graph is a dot plot showing beverage prices most

1. **State the problem:** We want to construct a 97% confidence interval for the average outstanding balance of credit cards based on a sample of 80 customers. 2. **Identify the un

1. **Problem statement:** We have monthly rents of apartments that follow a normal distribution. A sample of 5 apartments is given with sample mean $b$. We want to find the confide

1. **Stating the problem:** We have monthly rents for 5 apartments: 1901, 2089, 1502, 2149, and 2192 euros. We want to analyze these rents. 2. **Calculate the mean (average) rent:*

1. **Problem:** Find the range of the data set given the minimum is 15 and the maximum is 65. 2. **Formula:** The range of a data set is calculated as:

1. **State the problem:** Determine whether the broadcaster's comment about the away team winning 6 consecutive meetings on full moon nights is based on observational or experiment

1. **State the problem:** We are analyzing a study about colon cancer screening programs and their effect on death rates from colon cancer.

1. **Problem Statement:** You roll a fair die $n=115$ times. Each roll is a success if the top side shows a 6, failure otherwise. Let $X$ be the number of successes (6s).

1. **Problem statement:** You roll a fair die $n=115$ times and count the number of times $X$ the top side shows a 6.

1. **State the problem:** We have a data set with values: 154, 151, 173, 208, 147, 175, 175, 163, 56, 156. The value 208 is identified as a stray (outlier).

1. **State the problem:** We are given a stem-and-leaf plot representing club sizes and a frequency table with some missing values. We need to fill in the missing frequencies for t