📊 statistics

1. **Problem Statement:** Estimate the linear regression model $$Y = \beta_1 + \beta_2 X_2 + \beta_3 X_3 + U$$ using the given summary statistics for $N=9$ observations.

1. Problem: Given the average TV viewing hours per household per week is 50.4 hours with a standard deviation of 11.8 hours and a sample size of 42 households. 1.a. Find the probab

1. The problem asks about the number of people who did not like any flavor. 2. To find this, we need the total number of people surveyed and the number of people who liked at least

1. **State the problem:** We need to find the ratio of software engineers proficient in Python to those proficient in Java from a sample of 200 engineers. 2. **Identify given data:

1. **State the problem:** We are given 20 data points representing the number of cardiograms performed each day. We need to construct a stem-and-leaf plot with leaves arranged in o

1. **Problem 1: Testing if proportions of shoppers preferring stores A, B, C, D, and E are the same** Given data:

1. **Problem 1: Testing if proportions of shoppers preferring stores A, B, C, D, and E are the same** Given data: Total shoppers = 1100

1. **Representation of Data Formulas:** - Mean (Arithmetic Mean): $$\bar{x} = \frac{\sum x_i}{n}$$ where $x_i$ are data points and $n$ is the number of points.

1. **State the problem:** A researcher wants to test if the fat content of a processed food exceeds 30% based on a sample of size $n=7$ with values 31.5, 30.3, 31.1, 30.7, 29.9, 29

1. The problem asks to construct appropriate null and alternative hypotheses for the claim that the mean lifetime of LED lights is 10,000 hours. 2. The null hypothesis ($H_0$) usua

1. The problem asks us to determine which construction of null hypothesis ($H_0$) and alternative hypothesis ($H_1$) is correct given that the population mean is 36. 2. Statement i

1. The problem asks us to determine which construction of null and alternative hypotheses is correct given that the population mean is 36. 2. Statement i says:

1. The problem asks us to determine which construction of null hypothesis ($H_0$) and alternative hypothesis ($H_1$) is correct given that the population mean is 36. 2. For hypothe

1. **State the problem:** We want to find the 95% confidence interval for the population mean gas mileage of hybrid cars. 2. **Given data:**

1. **Preliminary Analysis: Qualitative Variables** To describe the composition of the sample with respect to each qualitative variable, we calculate the frequency and relative freq

1. **State the problem:** We need to construct a categorical frequency distribution for the given data on how much trust people place in the information they read on the Internet.

1. **State the problem:** We have a data sample of size $n=6$ with values: 7, 4, 9, 7, 3, 12. 2. **Order the data:** Sort the data from smallest to largest:

1. Problem: Classify variables as categorical or numerical, and if numerical, as discrete or continuous, and identify the measurement scale. 1.a Number of telephones per household:

1. The problem asks for the area (probability) between the z-scores $-1.73$ and $0.49$ on the standard normal distribution curve. 2. The area under the standard normal curve betwee

1. The problem states that for a standard normal distribution $Z$, we want to find the value $z^*$ such that $P(Z \geq z^*) = 0.025$. 2. Since the total area under the normal curve

1. **State the problem:** We have a cumulative frequency curve for the lengths of 80 bananas. We want to find: