 # Data modeling questions and answers

Recent questions in Modeling data distributions wurmiana6d 2021-11-19 Answered

### Ron Larson - Calculus 11th Edition Chp 3.3 Increasing and decreasing functions and the first derivative test. Please show work and explain steps, thank you. Modeling Data. The end-of-year assets of the Medicare Hospital Insurance Trust Fund (in billions of dollars) for the years 2006 through 2014 are shown. 2006: 305.4 2007: 326.0 2008: 321.3 2009: 304.2 2010: 271.9 2011: 244.2 2012: 220.4 2013: 205.4 2014: 197.3 (Source: U.S. Centers for Medicare and Medicaid Services) (b) Use a graphing utility to plot the data and graph the model. veudeje 2021-11-19 Answered

### The data for the joint probability mass function of X and Y (two different measurement systems) are given in the table below. a) Calculate the marginal distributions of X and Y and plot them. b) Select one of the Y values from the table and find the conditional probability mass function of X for that Y value you have selected and plot it. c) Show whether X and Y are independent or not. d) Calculate the covariance of (X,Y) i.e. Cov(X,Y). \begin{array}{|c|c|}\hline f(x,y) & 1 & 2 & 3 & 4 \\ \hline 10 & 0.05 & 0 & 0.1 & 0 \\ \hline 20 & 0.1 & 0.1 & 0.05 & 0.05 \\ \hline 30 & 0.05 & 0 & 0.15 & 0 \\ \hline 40 & 0.1 & 0.15 & 0.05 & 0.05 \\ \hline \end{array} puntgewelb5 2021-11-18 Answered

### The Great White Shark. In an article titled “Great White, Deep Trouble” (National Geographic, Vol. 197(4), pp. 2–29), Peter Benchley—the author of JAWS—discussed various aspects of the Great White Shark (Carcharodon carcharias). Data on the number of pups borne in a lifetime by each of 80 Great White Shark females are provided on the WeissStats site. Use the technology of your choice to a. obtain frequency and relative-frequency distributions, using single-value grouping. b. construct and interpret either a frequency histogram or a relativefrequency histogram. lilyta79jd 2021-11-18 Answered

### Look at the normal curve below, and find $$\displaystyle\mu,\ \mu+\sigma$$, and $$\displaystyle\sigma$$ $\begin{array}{|c|c|}\hline \mu & = & \\ \hline \mu+\sigma & = & \\ \hline \sigma & = & \\ \hline \end{array}$  pavitorj6 2021-11-18 Answered

### The data for the joint probability mass function of X and Y (two different measurement systems) are given in the table below. a) Calculate the marginal distributions of X and Y and plot them. b) Select one of the Y values from the table and find the conditional probability mass function of X for that Y value you have selected and plot it. c) Show whether X and Y are independent or not. \begin{array}{|c|c|}\hline f(x,y) & 1 & 2 & 3 & 4 \\ \hline 15 & 0.1 & 0 & 0.1 & 0.05 \\ \hline 20 & 0.05 & 0.05 & 0 & 0.1 \\ \hline 25 & 0 & 0.05 & 0.05 & 0.1 \\ \hline 30 & 0.1 & 0.05 & 0.15 & 0.05 \\ \hline \end{array} d) Calculate the covariance of (X,Y) i.e. Cov(X,Y). generals336 2021-10-27 Answered

### Which of the following is nota condition for constructing a confidence interval to estimate the difference between two population proportions? A. The samples must be selected randomly. B. The data must come from populations with approximately normal distributions. C. When samples are taken without replacement, each population must be at least 10 times as large as its corresponding sample. D. The samples must be independent of each other. E. The observed number of successes and failures for both samples must be at least 10. DofotheroU 2021-10-26 Answered

### A standard 3 sigma x-bar chart has been enhanced with early warning limits at plus-minus one sigma from the centerline . Three sample means in a row have plotted above the +1 sigma line . what is the probability of this happening if the process is still in control. Chesley 2021-10-26 Answered

### A random sample of $$\displaystyle{n}_{{1}}={14}$$ winter days in Denver gave a sample mean pollution index $$\displaystyle{x}_{{1}}={43}$$. Previous studies show that $$\displaystyle\sigma_{{1}}={19}$$. For Englewood (a suburb of Denver), a random sample of $$\displaystyle{n}_{{2}}={12}$$ winter days gave a sample mean pollution index of $$\displaystyle{x}_{{2}}={37}$$. Previous studies show that $$\displaystyle\sigma_{{2}}={13}$$. Assume the pollution index is normally distributed in both Englewood and Denver. (a) State the null and alternate hypotheses. $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}{>}\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}{<}\mu_{{2}};\mu_{{1}}=\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}{<}\mu_{{2}}$$ $$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}};\mu_{{1}}\ne\mu_{{2}}$$ (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population distributions are approximately normal with known standard deviations. The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. (c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to two decimal places.) (d) Find (or estimate) the P-value. (Round your answer to four decimal places.) (e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha? At the $$\displaystyle\alpha={0.01}$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the $$\displaystyle\alpha={0.01}$$ level, we reject the null hypothesis and conclude the data are statistically significant. At the $$\displaystyle\alpha={0.01}$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the $$\displaystyle\alpha={0.01}$$ level, we reject the null hypothesis and conclude the data are not statistically significant. (f) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver. Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. (Round your answers to two decimal places.) lower limit upper limit (h) Explain the meaning of the confidence interval in the context of the problem. Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver. Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver. Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver. SchachtN 2021-10-23 Answered

### How do frequency tables, relative frequencies, and histograms showing relative frequencies help us understand sampling distributions? They show each data point in the sampling distribution and how it relates to the overall distribution.They provide insight into the overall behavior of the population, therefore helping us understand the sampling distribution. They help us visualize the sampling distribution by using tables and graphs that approximately represent the sampling distribution.They help us visualize the sampling distribution by using tables and graphs that approximately represent the population distribution. beljuA 2021-10-22 Answered

### Let x be a continuous random variable with a standard normal distribution. Using the accompanying standard normal distribution table, find $$\displaystyle{P}{\left({x}\geq{2.26}\right)}$$ beljuA 2021-10-20 Answered

### The population mean may be reliably estimated using a statistic calculated from data recorded from randomly selected individuals.’ Explain this statement with reference to sampling distributions and the central limit theorem. Alyce Wilkinson 2021-10-20 Answered

### Range=max value- min value h=r/m m=no of classes The weights shown in data given to the nearest tenth of a pound, were obtained from a sample of 18- to 24-year-old males. Organize these data into frequency and relative-frequency distributions. Use a class width of 20 and a ﬁrst cutpoint of 120. 129.2 185.3 218.1 182.5 142.8 155.2 170.0 151.3 187.5 145.6 167.3 161.0 178.7 165.0 172.5 191.1 150.7 187.0 173.7 178.2 161.7 170.1 165.8 214.6 136.7 278.8 175.6 188.7 132.1 158.5 146.4 209.1 175.4 182.0 173.6 149.9 158.6 Also calculate cumulative frequency and midpoint. Zoe Oneal 2021-10-20 Answered

### List 7 ways of representing data he298c 2021-10-18 Answered

### Solve the following If the join probability distribution of X and Y iss given by $$\displaystyle{f{{\left({x},{y}\right)}}}={\frac{{{x}+{y}}}{{{30}}}}$$ f or $$\displaystyle{x}={0},\ {2},\ {3}:$$ $$\displaystyle{y}={0},\ {1},\ {2}$$ Find a) $$\displaystyle{P}{\left({X}\leq{2},\ {Y}={1}\right)};$$ b) $$\displaystyle{P}{\left({X}{>}{2},\ {Y}\leq{1}\right)};$$ c) $$\displaystyle{P}{\left({X}{>}{Y}\right)};$$ Khadija Wells 2021-10-17 Answered

### Reporting summary measures such as the mean, median, and standard deviation has become very common in modern life. Many companies, government agencies will report these descriptive measures of a variable, but they will rarely provide information on the shape of the distribution of that variable. In previous tutorials, you have learned some basic properties of some distributions that can help you to decide if a specific type of distribution is a good fit for a set of data. According to the National Diet and Nutrition Survey: Adults Aged 19 to 64, British men spend an average of 2.15 hours per day in moderate or high intensity physical activity. The standard deviation of these activity times for this sample was 3.59 hours. Can we infer that these activity times could follow a normal distribution? The following may provide an answer. Suppose that the standard deviation for this sample was 0.70 hours instead of 3.59 hours, which make it numerically possible for the distribution to be normal. Again, considering the variable being measured, explain why the normal distribution is still not a logical choice for this distribution. emancipezN 2021-10-16 Answered

### Suppose we are testing $$\displaystyle{H}_{{{o}}}:{p}={0.20}$$ vs $$\displaystyle{H}_{{{a}}}:{p}$$ does not equal 0.20 and $$\displaystyle{T}{S}={2.34}$$. What is the p-value? iohanetc 2021-10-16 Answered

### MODELING REAL LIFE. You mix 0.25 cup of juice concentrate for every 2 cus of water to make 18 cups of juice. How much juice concentrate do you use? How much water do you use? $$\displaystyle{Y}{o}{u}{u}{s}{e}{B}\otimes\cup{s}{o}{f}{j}{u}{i}{c}{e}{c}{o}{n}{c}{e}{n}{t}{r}{a}{t}{e}{\quad\text{and}\quad}{B}\otimes\cup{s}{o}{f}{w}{a}{t}{e}{r}$$. Dolly Robinson 2021-10-16 Answered

### Learning math The Core Plus Mathematics Project (CPMP) is an innovative approach to teaching Math- ematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the performances of CPMP students with those taught using a traditional curriculum. In one test, students had to solve applied Algebra problems using calculators. Scores for 320 CPMP students were compared to those of a control group of 273 students in a traditional Math pro- gram. Computer software was used to create a confidence interval for the difference in mean scores. (Journal for Research in Mathematics Education, 31, no. 3) Conf level: 95% Variable: Mu(CPMP) – Mu(Ctrl) Interval: (5.573, 11.427) a) What’s the margin of error for this confidence interval? b) If we had created a 98% CI, would the margin of error be larger or smaller?c) Explain what the calculated interval means in context. d) Does this result suggest that students who learn Mathematics with CPMP will have significantly higher mean scores in Algebra than those in traditional programs? Explain. Lipossig 2021-10-14 Answered

### When establishing the differences between histogram and polygon: a) Which of the two diagrams is drawn with the help of class marks of a frequency distribution? b) Which of the two diagrams is drawn at the class boundaries of a frequency distribution? c) Which of the two diagrams contains a series of vertical rectangular bars? d) Which diagram is produced by connecting a set of consecutive points? e) Which of the two diagrams can be used to compare two or more data sets that are plotted according to the corresponding frequency distributions? Tyra 2021-10-14 Answered

### The following table summarizes the results of a study on SAT prep courses, comparing SAT scores of students in a private preparation class, a high school preparation class, and no preparation class. Use the information from the table to answer the remaining questions. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Treatment}&\text{Number of Observations}&\text{Sample Mean}&\text{Sum of Squares (SS)}\backslash{h}{l}\in{e}\text{Private prep class}&{60}&{680}&{265},{500.00}\backslash{h}{l}\in{e}\text{High school prep class}&{60}&{650}&{276},{120.00}\backslash{h}{l}\in{e}\text{No prep class}&{60}&{635}&{302},{670.00}\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Using the data provided, complete the partial ANOVA summary table that follows (Hint: T, the treatment total, can be calculated as the sample mean times the number of observations G, the grand total, can be calculated from the values of T once you have calculated them.) $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}{h}{l}\in{e}\text{Source}&\text{Sum of Squares (SS)}&{d}{f}&\text{Mean Square (MS)}\backslash{h}{l}\in{e}\text{Between treatments}&&&\backslash{h}{l}\in{e}\text{Within treatments}&&&\backslash{h}{l}\in{e}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ ANOVA summary tables typically have a "Total" row not induded in the partial table you just completed. Which of the following is a possible reason for induding this row? a) The $$\displaystyle{M}{S}_{{\to{t}{a}{l}}}$$ is used in the calculation of the F test statistic. b) The $$\displaystyle{S}{S}_{{\to{t}{a}{l}}}$$ is used in the calculation of the F test statistic. c) The total sums of squares is the sometimes called the "error term" d) The $$\displaystyle{S}{S}_{{\to{t}{a}{l}}}{i}{s}{s}{o}{m}{e}\times{e}{a}{s}{i}{e}{r}\to{c}{a}{l}{c}\underline{{a}}{t}{e}{t}{h}{a}{n}{P}{S}{K}{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}$$. Since $$\displaystyle{S}{S}_{{{w}{i}{t}{h}\in}}+{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}={S}{S}_{{\to{t}{a}{l}}}$$, you can use $$\displaystyle{S}{S}_{{\to{t}{a}{l}}}$$ to calculate $$\displaystyle{S}{S}_{{{b}{e}{t}{w}{e}{e}{n}}}$$. In ANOVA, the F test statistic is the ? of the between-treatments variance and the within-treatments variance. the value of the F test statistic is ? When the null hypothesis is true, the F test statistic is ? When the null hypotesis is false, the F test statistic is most likely ? In general, you should reject the null hypotesis for.

Statistics and probability also include various data modeling questions, which can be encountered basically everywhere from Social Sciences and Biology to Engineering and Data Science. Depending on your questions, you can receive immediate help by looking through the data modeling examples that we have presented below for you. These will help you to find solutions and find the answers to presented challenges. It is recommended to model your data carefully and to check things twice to ensure that everything is correct because accuracy is the key to any statistical work where a calculation is involved.
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