Recent questions in Modeling data distributions
Modeling data distributions

Nurses wondered if birth weights of babies are going up. They knew that the average bith weight ofa baby last year was 7.6 pounds. A random sample of 15 weights of babies atthe hospital where the nurses work gave an average birth weight of 7.9 pounds. Nurses felt thatthe birth Weights this year ware normally distributed. Which ofthe following is true about the distribution of sample means? Choose the correct answer below. A. Even though the sample size is less than 30, the distribution of sample means will be normal because the population data follow a normal distribution. B. The distribution of sample means will be normal regardless of the shape of the data in the population. C. Since the sample size is less than 30, the population data cannot be normally distributed. Therefore, the distribution of sample means will not be normally distributed. D. The distribution of sample means will not be normal even though the population data followed a normal distribution because the sample size is less than 30.

Modeling data distributions

Learning math The Core Plus Mathematics Project (CPMP) is an innovative approach to teaching Mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compare 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 program. Computer software was used to create a confidence interval for the difference in mean scores. (Journal for Research in Mathematics Education, 31, no. 3[2000]) 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.

Modeling data distributions

Suppose that you want to perform a hypothesis test based on independent random samples to compare the means of two populations. For each part, decide whether you would use the pooled t-test, the nonpooled t-test, the Mann– Whitney test, or none of these tests if preliminary data analyses of the samples suggest that the two distributions of the variable under consideration are a. normal but do not have the same shape. b. not normal but have the same shape. c. not normal and do not have the same shape. both sample sizes are large.

Modeling data distributions

What is modeling with linear equations?

Modeling data distributions

Continuous Probability Distributions The data records the length of stay of engineering students in the university. We will assume a uniform distribution between 5 to 7 years, inclusive. What is the probability that a randomly chosen engineering student will stay at most 6 years?

Modeling data distributions

Presenting data in the form of table. For the data set shown by the table, Solve, a) Create a scatter plot for the data. b) Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data. (If applicable, you will use your graphing utility to obtain these functions.) $$\begin{array}{|c|c|}\hline \text{Intensity (wattd per}\ meter^{2}) & \text{Loudness Level (decibels)} \\ \hline 0.1\text{(loud thunder)} & 110 \\ \hline 1\text{(rock concert, 2 yd from speakers)} & 120 \\ \hline 10 \text{(jackhammer)} & 130 \\ \hline 100 \text{(jet take off, 40 yd away)} & 140 \\ \hline \end{array}$$

Modeling data distributions

Give a real-life example of data which could have the following probability distributions. Explain your answers. a) uniform distribution b) exponential distribution c) bimodal distribution

Modeling data distributions

Determine whether each statement below is true or false All data distributions are normally distributed.

Modeling data distributions

True/False a) It is appropriate to use A Normal approximation for a Binomial distribution with $$\displaystyle{n}={15}$$ and $$\displaystyle{p}={0.2}$$ b) Both the Hypergeometric and the Binomial distributions deal with dichotomous (binary) data.

Modeling data distributions

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? You use ___ cups of juice concentrate and ___ cups of water.

Modeling data distributions

An alternative to the lognormal distribution for modeling highly skewed populations is the Pareto distribution with parameters θ and r. The probability density function is

Modeling data distributions

What are the data modeling concepts used in MongoDB? What are the main CRUD operations of MongoDB?

Modeling data distributions

What are the data modeling concepts used in column-based NOSQL systems and Hbase?

Modeling data distributions

In a normal distribution, a data value located 1 standard deviations below the mean has Standard Score: $$\displaystyle{z}=$$ In a normal distribution, a data value located 2.2 standard deviations above the mean has Standard Score: $$\displaystyle{z}=$$ In a normal distribution, the mean has Standard Score:$$\displaystyle{z}=$$

Modeling data distributions

Data such as "occupation" would use categorical frequency distributions: True and False?

Modeling data distributions

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) $$\displaystyle{P}{\left({X}{>}{Y}\right)}.$$

Modeling data distributions

a. Let $$\displaystyle{X}\sim{N}{\left({0},{1}\right)}{\quad\text{and}\quad}{E}\sim{N}{\left({0},{1}\right)}$$ be independent, and let $$\displaystyle{Y}={X}+\beta{E}$$. Show that $$\displaystyle{r}_{{{x}{y}}}={\frac{{{1}}}{{\sqrt{{\beta^{{2}}+{1}}}}}}$$ b.Use the results of part (a) to generate bivariate samples (x_i, y_i) of size 20 with population correlation coefficients −.9, −.5, 0, .5, and .9, and compute the sample correlation coefficients. c. Have a partner generate scatterplots as in part (b) and then guess the correlation coefficients.

Modeling data distributions

Answer true or false to each of the following statements and explain your answers. a. Polynomial regression equations are useful for modeling more complex curvature in regression equations than can be handled by using the method of transformations. b. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linearregression. c. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.

Modeling data distributions