Numerical Description Of The Outcome Of An Experiment I

A Numerical Description Of The Outcome Of An Experiment I

A numerical description of the outcome of an experiment is called a descriptive statistic probability function variance random variable QUESTION 2 1. A random variable that can assume only a finite number of values is referred to as a(n) infinite sequence finite sequence discrete random variable discrete probability function QUESTION 3 1. A random variable that may take on any value in an interval or collection of intervals is known as a continuous random variable discrete random variable continuous probability function finite probability function QUESTION 4 1. A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution random variance random variable expected value QUESTION 5 1.

The expected value for a binomial probability distribution is E(x) = Pn(1 - n) E(x) = P(1 - P) E(x) = nP E(x) = nP(1 - P) QUESTION 6 1. The variance for the binomial probability distribution is var(x) = P(1 - P) var(x) = nP var(x) = n(1 - P) var(x) = nP(1 - P) QUESTION 7 1. Which of the following is not a characteristic of an experiment where the binomial probability distribution is applicable? the experiment has a sequence of n identical trials exactly two outcomes are possible on each trial the trials are dependent the probabilities of the outcomes do not change from one trial to another QUESTION 8 1. The number of electrical outages in a city varies from day to day. Assume that the number of electrical outages (x) in the city has the following probability distribution. x f(x) 0 0.80 1 0.15 2 0.04 3 0.01 The mean and the standard deviation for the number of electrical outages (respectively) are 2.6 and 5..26 and 0. and 0. and 0.8 QUESTION 9 1.

The center of a normal curve is always equal to zero is the mean of the distribution cannot be negative is the standard deviation QUESTION 10 1. A normal distribution with a mean of 0 and a standard deviation of 1 is called a probability density function an ordinary normal curve a standard normal distribution none of these alternatives is correct QUESTION 11 1. A negative value of Z indicates that the number of standard deviations of an observation is to the right of the mean the number of standard deviations of an observation is to the left of the mean a mistake has been made in computations, since Z cannot be negative the data has a negative mean QUESTION 12 1. Which of the following is not a characteristic of the normal probability distribution?

The mean, median, and the mode are equal The mean of the distribution can be negative, zero, or positive The distribution is symmetrical The standard deviation must be 1 QUESTION 13 1. Z is a standard normal random variable. The P (1.41 ≤ Z ≤ 2.85) equals 0....0771 QUESTION 14 1. X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that X is between 1.48 and 15.56 is 0....9190 QUESTION 15 1.

Larger values of the standard deviation result in a normal curve that is shifted to the right shifted to the left narrower and more peaked wider and flatter Please use the excel sheet in working out the problems. Using the ROI data set: Please show each step in working out the problems 1. If we select 7 colleges from a major and then record whether they are of ‘School Type’ ‘Private’ or not, is this experiment a binomial one? Why or why not? 2.

For each of the 2 majors determine if the ‘Annual % ROI’ appears to be normally distributed. Consider the shape of the histogram and the measures of central tendency (mean and median) to justify your results. Report on each of these with charts and calculations to justify your answers. Business Major School Type Cost 30 Year ROI Annual ROI Private $222,700.00 $1,786,000.00 7.70% Private $176,400.00 $1,758,000.00 8.40% Private $212,200.00 $1,714,000.00 7.80% Public $125,100.00 $1,535,000.00 9.10% Private $212,700.00 $1,529,000.00 7.40% Public $92,910.00 $1,501,000..10% Private $214,900.00 $1,485,000.00 7.30% Private $217,800.00 $1,483,000.00 7.20% Private $225,600.00 $1,444,000.00 7.00% Private $217,300.00 $1,442,000.00 7.10% Private $226,500.00 $1,441,000.00 7.00% Private $215,500.00 $1,438,000.00 7.20% Private $223,500.00 $1,428,000.00 7.00% Private $226,600.00 $1,414,000.00 7.00% Private $189,300.00 $1,397,000.00 7.50% Public $89,700.00 $1,382,000.00 9.90% Public $87,030.00 $1,376,000..00% Private $218,200.00 $1,343,000.00 6.90% Private $229,900.00 $1,339,000.00 6.70% Private $148,800.00 $1,321,000.00 8.10% Best College ROI by Majo 2013: Payscale.com Engineering Major School Type Cost 30 Year ROI Annual ROI Private $221,700.00 $2,412,000.00 8.70% Private $213,000.00 $2,064,000.00 8.30% Private $230,100.00 $1,949,000.00 7.90% Private $222,600.00 $1,947,000.00 8.00% Private $225,800.00 $1,938,000.00 8.00% Public $87,660.00 $1,937,000..20% Private $224,900.00 $1,915,000.00 7.90% Private $221,600.00 $1,878,000.00 7.90% Public $125,100.00 $1,854,000.00 9.80% Private $215,700.00 $1,794,000.00 7.90% Public $92,530.00 $1,761,000..60% Private $217,800.00 $1,752,000.00 7.70% Public $89,700.00 $1,727,000..70% Private $229,600.00 $1,716,000.00 7.50% Public $101,500.00 $1,703,000..20% Public $115,500.00 $1,694,000.00 9.70% Public $104,500.00 $1,690,000..10% Public $69,980.00 $1,685,000..50%

Paper For Above instruction

The provided set of questions encompasses fundamental statistical concepts, including descriptive statistics, probability distributions, characteristics of binomial and normal distributions, and analysis of real-world data. This essay aims to elucidate these topics comprehensively, with particular emphasis on their definitions, properties, and applications, reinforced by examples derived from ROI datasets and experimental scenarios.

Understanding Descriptive Statistics and Random Variables

In the realm of statistics, a numerical description of the outcome of an experiment is termed a descriptive statistic. It summarizes data in a meaningful way, providing insights into the data set's central tendency, dispersion, and shape. A random variable is a variable whose values result from randomness within an experiment. Specifically, a finite random variable can assume only a limited set of outcomes, classified as a discrete random variable. Conversely, continuous random variables can take any value within an interval or collection of intervals, characterized by a continuous probability function.

Probability Distributions and Expectations

A probability distribution describes the likelihood of each possible outcome of a random variable, associating values with their respective probabilities. When dealing with binomial distributions, the expected value (or mean) is a key measure, calculated as E(x) = nP, where n is the number of trials, and P is the probability of success on each trial. The variance of a binomial distribution measures the spread of possible outcomes and is given by var(x) = nP(1-P).

Characteristics of Binomial and Normal Distributions

The binomial distribution is applicable under specific conditions: a fixed number of independent trials, two mutually exclusive outcomes per trial, and constant probabilities. An experiment violating these conditions, such as dependent trials or changing probabilities, is not binomial. In the provided examples, selecting seven colleges and recording whether they are 'Private' or not forms a binomial experiment when trials are independent and probabilities remain unchanged.

For normally distributed data, the distribution's shape is symmetric, with the mean, median, and mode coinciding. Notably, the standard normal distribution is characterized by a mean of 0 and a standard deviation of 1. Z-scores quantify how many standard deviations an observation is from the mean; negative Z values imply that the observation is below the mean.

Analyzing ROI Data and Distributional Assumptions

Using the ROI datasets, one can assess whether the 'Annual % ROI' for business and engineering majors follows a normal distribution. Visual tools like histograms, along with statistical measures such as mean and median, facilitate this assessment. For instance, if the histogram appears symmetric with a mean close to the median, and the data exhibits the classic bell-shaped curve, it suggests a normal distribution. Otherwise, skewness or kurtosis indicates deviation from normality.

Calculating these measures for each dataset reveals typical characteristics: a close alignment of mean and median, symmetry of the histogram, and the presence of outliers or skewness. Such analysis guides decisions on statistical tests or modeling assumptions—a crucial step in empirical research.

Effects of Standard Deviation on Distribution Shape

Larger standard deviations cause the normal curve to appear wider and flatter, indicating increased variability. Conversely, smaller standard deviations produce narrower, more peaked distributions. These properties are fundamental in understanding and interpreting data variability and are vital in applications such as risk assessment or quality control.

Concluding Remarks

In sum, understanding the statistical concepts covered enables effective data analysis and interpretation. Recognizing experiment types, distribution properties, and data characteristics fosters accurate modeling and decision-making in research and real-world applications. The ROI datasets exemplify the application of these principles, illustrating how statistical analysis informs strategic choices in education investments and beyond.

References

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  • Payscale.com (2013). Best College ROI by Major. Retrieved from https://www.payscale.com
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