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The basic question we want to answer is whether less energy would be expended (and less work involved) if the woman brought her groceries upstairs by making a single trip, carrying all three bags at once, or if she made multiple trips, carrying one bag at a time (or two bags on the first trip and one bag on a second trip). Work is defined as F × d, the force multiplied by distance, or ΔE, the change in energy. The change in energy experienced in this problem is a change in potential energy, so W = ΔE = mgΔh.

First scenario: one trip carrying all three bags at once

m = ...

Summary stats:

i) Mean µ = 1nx = 113 (6 + 26 + 28 + 30 + 32 +34 + 39 + 41 + 46 + 46 + 68 + 100 + 124 + 132) = 113 (706) = 54.3077 ii) Median = Middle (x) = 39 iii) Standard deviation σ = 1n i=1n(x₁–µ)² Standard deviation σ = 113 (18976.7695) = 38.2067 iv) Inter quartile Range = Q₃ - Q₁

6, 26, 28, 30, 32, 34, 39, 41, 46, 68, 100, 124, 132

Q₃ = 34n = 34 13 = 9.75th term = 12 (68 + 100) = 84 Q₁ = 14n = 14 13 =3.25th term = 12 (28 + 30) = 29 IQR= 84 – 29 = 55 v) Range = Max x – Min x = 132 - 6 = 126

Distribution of the data

The mean is more than the median indicating that the data is not normally distributed and is positively skewed. This implies ...

Statistical hypothesis testing is a very important concept in statistics. There are steps to be followed in hypothesis testing, as shown below (Eberly College of Science, n.d.) Formulation of the Null Hypothesis – this step involves stating of the null hypothesis, which states equality between the hypothesized value and a predicted value. In this case, it is the opposite of the alternative hypothesis.

H0: The average salary for all jobs in Minnesota is greater than or equal to $65,000.

H0: x ≥$65,000 Formulation of the Alternative Hypothesis –the alternative hypothesis is the opposite of the null hypothesis, which states that a value is less than, greater than, or not equal to a certain value. This ...

Importance of Confidence intervals

The confidence interval is a set or range of values that a population parameter is likely to fall within (Graham, 2008). It is calculated using the sample statistics and a given confidence level. For instance, a confidence interval of the mean calculated using the sample statistics, gives the lowest and highest possible value of the population mean. The population mean is expected to be within the confidence interval. A point estimate is a single value that approximates a population parameter (Graham, 2008). For instance, a sample mean is point estimate of the population mean, while a sample proportion is ...

Overview of the scenario

The scenario involves analyzing the distribution of salaries for different jobs in the state of Minnesota. The client is interested in the distribution of salaries for jobs with salaries ranging from $40,000 to $120,000. Data on 364 different jobs in the state were collected from the Bureau of Statistics. The data will be analyzed by determining the measures of central tendency and dispersion to understand the distribution of salaries.

Quantitative and qualitative variable

In this scenario, the job title is the qualitative variable since it cannot be measured numerically. On the other hand, salary is the quantitative variable since it is ...

Analysis, Interpretation and Presentation of Data

Background of the Study In this study, a researcher measured the performance of students before and after an 8-week Moodle based tuition. The study was formed of 25 undergraduate students,who had to be enrolled in the final year of the degree programme. The effectiveness of Moodle based tuition was considered by many previous researches. The researchers from the University of Patras studied students’ performance and practices, while using the Moodle system in their learning environment. 117 students were involved in this study. The methodology of the study was a problem solving course. The results of the study were ...

The Mars Climate Orbiter: A Multimillion Dollar Mistake

The Story Grossman (1999) addresses the incident of NASA’s Mars Climate Orbiter in her article named “Metric Math Mistake Muffed Mars Meteorology Mission”. She explains how a simple unit conversion mistake caused the Orbiter to burn up in the Martian atmosphere. The vessel costed NASA a whopping $125 million when it vanished into the Martian atmosphere. The problem, later identified by a NASA review board, owed to a software glitch. The software was used to calculate the thrust in “pounds of force” while the other software took the input in “newtons”. This happened due to the fact that ...

Problem 1. Yowie

Part 1 The first stage was actually taking all the required physical measurements of all the group participants. They can be found in Tab.1: The only ratio we were familiar with was the one proposed by the assignment (height : arm span = 1 : 1), so we checked it. Based on our measurements we were able to make a conclusion that this ratio is actual but not precise. In our data, the ratios were: Courtney 167 : 160 = 1.04 : 1, Angela 169 : 170 = 1 : 1.01, Steev 176 : 180 = 1 : 1.02, Danielle 155 : 150 = ...

Costco Wholesale Corporation is a leading merchandise firm that engages in the sale of a vast range of products ranging from electronics, household ware, and machinery to office ware. Costco recorded a profit of $27 million to merchandise costs resulting from deflationary trends in both 2015 and 2013 (Stock Analysis, 2016). However, in 2014, net inflationary trends caused a benefit of $28 million recorded to merchandise costs (Stock Analysis, 2016). This amplified the cumulative LIFO (Last-in, first-out) valuation of merchandise as at the close of 2015 and 2014, the aggregate effect of the LIFO valuation of merchandise stood at $ ...

1. Personal Annual Income

The personal annual income is $19,200.

2. Monthly Payment a) The monthly amount is found by dividing the annual income by 12: $19,200 / 12 = $1,600. b) The monthly payment is maximum 33% of the monthly income, which is: $1,600 ∙ 33% = $1,600 ∙ 0.33 = $528.00. c) Maximum required payment (monthly payment minus fees): $528.00 / 1.15 = $459.13.

This is the maximum amount that a person can afford to pay each month for a home loan.

3. Loan Amount Using the Excel table, the maximum amount for home loan was found for monthly payment $459.13 at 4.18% APR for 30 years. This amount is $94,113.00. Thus, a person can afford a house for about $94, ...

One of the contentious topics that is sure to spark discussion nowadays is the issue of the difference between natural US citizens and immigrants. Some feel that immigrants are different from natural US citizens in some aspects, and these differences lead to ruin of the American economy and society. Others maintain that there is no significant difference between the two and as such they should be treated more or less the same. Immigrants and US citizens can be compared in different ways, one of which being the topic of domestic violence. Domestic violence is an umbrella term for any ...

Introduction

In this report, we will critically analyze and summarize an interesting research work (Chachi, Taheri, and Viertl) related to testing statistical hypothesis when relevant data and confidence intervals are not precise. In classical Statistical inferences, we state a Null hypothesis about a precise parameter. Then, we test the validity of the Null hypothesis using classical Statistical tests using the concept of confidence intervals at some predefined level x (say 5%) based on uncertainty we can tolerate. If the value of the testing parameter lies in confidence interval 1-x, then the Null hypothesis cannot be rejected. If testing results shows ...

Information:

Wasatch Front is in Utah, U.S. Intensity (Lambda) = 1 earthquake every 350 years Length (u) = life expectancy in Utah is 80 years / earthquake interval (“"Utah Life Expectancy") = 80 / 350 = 1/4.375 = 0.2286

Problem:

The problem is: What is the probability of experiencing an earthquake within the Utah lifetime of 80 years? P (x=1, u=0.2286) = e (−0.2286) * (0.2286)1 1! = 0.796 * 0.182 1 = 0.182 ("Poisson Distribution") The probability is 18.2% which means that anyone just born and would be staying in Utah would have this chance to experience a major earthquake along the Wasatch Front.

Which kinds of businesses or organizations should spend resources to prepare for an earthquake?

The first kind includes those ...

1. a. i. -5log749+4log55-6log42 =-5log777+4log5512-6log4412 =-(5)(7)log77+412log55-612log44 =-571+4121-6121 =-35+2-3=-36 ii.log7343x16807y =log7343x-log716807y =log773x-log775y =3xlog77-7ylog77 =3x-7y b. 122×5×3-71024 ×5-3-2 =12-4×5-2×3141024-22×56=4-4×3-4×3141024-1×56+2=2-8×3102-10×58=3102-10+8×58=2231058 c. The graph is shown in the next figure:

2 a. 2x=1024 2x=210→x=10 i. 7292x-3=6561 362x-3=38 62x-3=8 12x-18=8 12x12=2612→x=136 iii. log23x+1=4 3x+1=24 3x+1=16 3x3=153→x=5 b. The slope of the line 2x+y=4 is: y=-2x+4→m=-2 The equation of the line passing through (-1,4) parallel to 2x+y=4 is: y-y1=mx-x1→y-4=-2x--1 y-4=-2x-2→y=-2x+2 ...

In this paper, the importance and the application of probability and statistics tools to a real world problem will be considered. My goal is to investigate if the hours that students studied and the grade they earned on a test are related factors. The sample provided contains the data of 30 students. Their hours of study and exam scores are recorded and given in the spreadsheet. In order to determine the strength of the association, I will use Pearson’s correlation coefficient. The correlation reflects the statistical association between random variables. If the variables are related, a change in ...

Percentages are very useful in day to day activities and can be a handy way of writing fractions, making comparisons and describing change. For example, in a class test where a student scores 7 points out of a possible 10, and as a fraction, this is expressed as 7/10. The same can also be expressed as a percentage where the fraction 7/10 is multiplied by 100 percent. In this case 7/10*100%= 70%. Therefore, the student scored 70 percent of the total mark in the test. On the other hand, percentages can also be used to describe change. For ...

The Pythagorean Theorem can be used to solve numerous real world problems involving right-angled triangles where the lengths of at least two sides are known. One of the areas the theorem can be applied is in construction by painters. Since painters use ladders to reach high walls, the Pythagorean theorem would assist them in determining how tall their ladder should be in order for its base to be safely placed away from the wall such that it is stable and does not tip over. The walls are perpendicular to the ground, and the ladder is a hypotenuse, and this ...

1. Assume initial population of 2700, rate of growth of 6%, and time interval of 15 years. The formula to be used is also called continuous growth formula . The future value is: FV=PV×ert PV=2700, r=0.06, t=15 FV=2700×e0.06×15=6640 2. For time intervals 30 and 45: PV=2700, r=0.06, t=30, 45 FV=2700×e0.06×30=16334 FV=2700×e0.06×45=40175 3. For growth rates 8% and 10%: PV=2700, r=0.08, t=15,30, 45 FV=2700×e0.08×15=8964 FV=2700×e0.08×30=29763 FV=2700×e0.08×45=98815 PV=2700, r=0.10, t=15,30, 45 FV=2700×e0.10×15=12100 FV=2700×e0.10×30=54230 FV=2700×e0.10×45=243050

The results from calculations are similar to the results coming from the Excel file.

4. The graphs are not straight ...

Math Assignment

1. Original Condo fees for bigger condos = $500 per year

Reduction by $200 per year. Owners of big Condos share costs by 4.5% = 4.5% of $300 = $13.5 Fee paid by large condo owners = $313.5 which is comparatively greater than small condo owners. Hence, the challenger is telling the truth. 2. Distance travelled by the car = 1.1 miles Time taken = 57.51 sec. = 57.51/3600 hours = 0.015975 hours Speed of the car = Distance travelled/Time taken = 1.1/0.015975 = 68.85758998435055miles per hour.

There are 16 significant digits in determining the speed of the car.

3. Time taken to reach Mom’s house = 22 min. Time stuck in traffic = 3.18 min. Time to be taken to reach Mom’ ...

MATH221

Statistical Concepts: Probability Binomial Probability Distribution Calculating Binomial Probabilities Open a new Excel worksheet. Open spreadsheet In cell A1 type “success” as the label Under that in column A, type 0 through 10 (these will be in rows 2 through 12) In cell B1, type “one fourth” In cell B2, type “=BINOM.DIST(A2,10,0.25,FALSE)” [NOTE: if you have Excel 2007, then the formula is BINOMDIST without the period]

Then copy and paste this formula in cells B3 through B12

In cell C1, type “one half” In cell C2, type “=BINOM.DIST(A2,10,0.5,FALSE)”

Copy and paste this formula in cells C3 through C12

In cell D1 type “three fourths” In cell D2, type “=BINOM.DIST(A2,10,0.75, ...

1. The paper (BP Global, 2016) aims to describe the world energy consumption and present the trends in the industry. The population is the oil, natural gas, coal, nuclear energy, hydroelectricity, renewable and primary energy use of various countries. The paper is a descriptive review. 2. The research is provided by BP Global, which has been performing the energy reviews for 65 years. Therefore, the methodology is well-developed and the research is unbiased (Thiessen, 2013). 3. The data are based on the figures presented by the governments, and thus are reliable. The sample is based on processing the numerical ...

Quality assurance is an mportant part of the production and a guard of company reputation. Quality control engineers work all year round, yet their role is of particular significance when the claims of inappropriate quality appear. The current problem is associated with lack of soda in soda bottles. The company advertises 16 ounces; however, there are accusations that there are less soda in the bottles. The quality engineer has to run an investigation. Therefore, the plan of the research is as follow. It is definitely impossible to test all the produced bottles. The statistical methods address the issue. The ...

Introduction

In the field of social and psychological research, the development of research tools to measure phenomena by attributing quantitative values to them and developing them into continuous variables is a crucial part of data collection and understanding of the phenomena. The reliability and validity of the measuring instruments thus developed is of utmost importance in establishing the value and capability of the constructs. We all can relate to our personal or friends and peers’ childhood experiences of anxiety as a child. The children are more vulnerable as a result of anxiety situations as they have little or no idea ...

Question 1

a) Random sampling is a method of sampling in which each member of a population has equal chances of being included into the sample. Each member of the sample is chosen entirely by chance. Since each member has equal chances, one advantage of the random sampling method is that it is fair and unbiased. The random sample chosen can properly represent the population it is taken from. One disadvantage of random sampling is that there is no systematic approach in choosing the sample. If the population being studied becomes larger, the fairness of the random sampling method becomes more ...

.GSS 2014 Statistical Analysis: Written up Assignment

Introduction

The GSS 2014 has been established with the view to generate ongoing research data on demographics of the country for social welfare and decision making. The General Social Surveys (GSS) have been conducted by the National Opinion Research Centre (NORC) annually since 1972, except for the years 1979, 1981, and 1992, and biennially beginning in 1994. The GSS surveys are supposed to be part of a social indicator research, applying questionnaire items and wording in order to facilitate time-trend studies. There are a total of 3,842 cases in the data set. ...

Which dataset did you choose?

I selected “Unemployment rates” dataset.

Run descriptive statistics in the Analysis Toolpak.

Create and insert at least 2 charts that portray your data, for example bar chart showing the difference between the groups, or line graph showing the relationship between two variables.

Bar chart:

Scatter plot: What is your null hypothesis about the data? There is no linear relationship between the unemployment rates of college and high school graduates in 2000 – 2011. What is your alternative hypothesis? There is a significant linear relationship between the unemployment rates of college and high school graduates in 2000 – 2011 Choose the appropriate test to run (one-sample z, t-test, ANOVA, linear regression, ...

Introduction

This paper seeks to conduct an analysis for the financial performance of the Toyota Motor Corporation and General Motors Company for their financial years ended in 2015. In order to arrive at objective results, the analysis will compare different financial and performance ratios for both businesses. It is a purely objective analysis that will be based on the figures presented on the annual audited final accounts of the companies.

A.Ratios

Liquidity ratios These are financial metrics used to assess and determine an entity’s ability to meet its short term debt obligations. They include:

Current ratio

Quick ratio/Acid test ratio Profitability ratios. ...

The problem of the exchange rate differences between different currencies is the special issue to be defined in the process of estimation of the company real value. The interrelation dollar-sterling equals approximately 1.5 % as for the 1983 year. This correlation means that the pound sterling is devaluated currency comparing to dollar. The worth of the pound sterling is higher than that of the dollar. It is well-known fact that the stronger is the currency the more profitable are the investments made in this currency. From this only statement and the dollar/pound correlation we may make the conclusion that the ...

Introduction

Fluctuations in consumption are an important cause of cyclical fluctuations in the economy, so the analysis of the theory of consumer demand helps to study macroeconomics laws in many ways. It allows you to determine the effect on national consumption, savings and investments, their relation to the national income. The theory of consumer behavior was developed by George. M. Keynes. It has a leading position in the macroeconomic theory as an important tool of economic analysis. The national consumption and national savings account for a total after-tax income of a population. A national consumption is the amount of money ...