📊 statistics

1. **Problem statement:** We want to test the null hypothesis $H_0: \rho=0$ against the alternative $H_1: \rho=0.5$ for the correlation $\rho$ between heights $(X_i, Y_i)$ of sibli

1. **State the problem:** We have a list of midterm test scores and need to find the lowest score that is above the 80th percentile, which means the lowest score that is higher tha

1. The problem asks which sample method is least likely to produce biased results in a survey comparing the popularity of different sports at a school. 2. Bias in sampling occurs w

1. **State the problem:** Paula recorded the number of phone calls she received each day over a period of consecutive days. We need to find: a) The total number of days the survey

1. **Problem statement:** Paula recorded the number of phone calls she received each day over a period of consecutive days. We need to find: a) The total number of days the survey

1. **Problem Statement:** Paula recorded the number of phone calls she received each day over a period of consecutive days. We need to find: a) The total number of days the survey

1. The problem is to analyze the given list of numbers: 10,150; 6,300; 9,900; 38,500; 10,851; 9,450; 5,200; 10,000; 4,300; 11,700; 10,500. 2. Since no specific question is asked, l

1. The problem is to analyze the given list of numbers: 10150, 6300, 38500, 10851, 9450, 10000, 4300, 9200, 9900, 11700, 10500. 2. Since no specific question is asked, let's find s

1. The problem asks to distinguish between discrete and continuous variables and how to write their possible values correctly. 2. Discrete variables take countable values, often in

1. The problem asks to identify the correct possible values for discrete and continuous variables based on the descriptions given. 2. Discrete variables take countable values, ofte

1. **State the problem:** We are given the mean $\mu = 70$ and variance $\sigma^2 = 4$ of exam grades. Allan scored $X = 87$. We need to find Allan's z-score, which tells us how ma

1. **State the problem:** We are given a sample of costs for a 30-second spot on various cable networks and need to find the sample standard deviation, rounded to two decimal place

1. The problem asks to find the correlation coefficient given the coefficient of determination. 2. The coefficient of determination, denoted as $R^2$, is related to the correlation

1. **State the problem:** We are given a sample of annual rainfall data (in millimeters) for Australia from 1983 to 2002 and need to compute the sample variance. 2. **Recall the fo

1. The problem asks which type of graph is most appropriate to visualize how many students scored below 60% in a test. 2. Let's analyze each option:

1. **Problem Statement:** We have 13 jurors randomly selected from a population of 5 million residents, where 48% are minorities. Among the 13 jurors, 2 are minorities.

1. The problem involves interpreting a circle graph that shows the favorite types of pets in a community. 2. (a) To find which category was chosen by approximately one-eighth of th

1. The problem asks to identify types of data: qualitative vs quantitative, discrete vs continuous. 2. Qualitative data describes qualities or categories (non-numeric), while quant

1. **Problem Statement:** Given grouped data with class intervals, frequencies, midpoints, relative frequencies, fx (frequency times midpoint), and cumulative frequencies, find the

1. **State the problem:** We need to find the mean (average) of the numbers 54, 38, 52, 51, 49, 46, 39, 53, 47, 42, 52, and 41. 2. **Formula for the mean:** The mean of a set of nu

1. **Stating the problem:** We have maximum heart rates (beats per minute) recorded for four different workouts, each with five values. We want to analyze these data points, possib