A software company develops and markets a popular business simulation/modeling program. A random number generator contained in the program provides random values from various probability distributions. The software design group would like to validate that the program is properly generating random numbers. Accordingly, they generated 5,000 random numbers from a normal distribution and grouped the results into the accompanying frequency distribution shown below. The sample mean and sample standard deviation are 90 and 10, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table) Value Frequency Under 60 60 up to 70 70 up to 80 80 up to 90 90 up to 100 100 up to 110 110 up to 120 120 or more 109 682 1,757 1,694 649 94 Total = 5,000 a. Using the goodness-of-fit test for normality, state the competing hypotheses to test if the random numbers generated do not follow the normal distribution.

A software company develops and markets a popular business simulation/modeling program. A random number generator contained in the program provides random values from various probability distributions. The software design group would like to validate that the program is properly generating random numbers. Accordingly, they generated 5,000 random numbers from a normal distribution and grouped the results into the accompanying frequency distribution shown below. The sample mean and sample standard deviation are 90 and 10, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table) Value Frequency Under 60 60 up to 70 70 up to 80 80 up to 90 90 up to 100 100 up to 110 110 up to 120 120 or more 109 682 1,757 1,694 649 94 Total = 5,000 a. Using the goodness-of-fit test for normality, state the competing hypotheses to test if the random numbers generated do not follow the normal distribution.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. Assume that the data are from normally-shaped distributions which have equal variances. The results are shown in the table below. Round all answers to 4 decimal places. Group A 105 101 103 104 109 Group B Group C 149 173 156 149 124 124 a. What is the F Statistic? b. What is the p-value? 190 194 102 102
2. A department store receives an average of 5 returned items per day. The probability that a returned item has an available replacement is 0.65. [Hint: there are two separate distributions here.] d. e. f. Calculate the probability that there are 4 returned items and none has available replacements in a certain day. Calculate the variance and the mean of the returned items. Calculate the variance and the mean of the replaced items. 2
4. Review the variance function for specific distributions. For Bernoulli, Poisson, Gamma, and Inverse Gaussian, what does the variance function say about our ability to predict the range of possible values? (This may be a little bit challenging; give it your best guess.)
Part a,b and c have been answered, this is for part d now.
A box contains 5 green and 3 orange balls. If three balls are taken at random with replacements, what is the variance number of orange balls? A. 45/8 B. 15/8 C. 1/8 D. 9/8
Part C
No Excel spreadsheets, please. I need to see the work to better understand the material.
Answer a, b, & c.
Consider the following problem where we work for an oil company that looks for oil in geographic formations that are favorable to the formation of oil. Find the expected value for barrels of oil in problem A and then find the variance and standard deviation. For B, find the mean, variance, and standard deviation using formulas. For variance and standard deviation, use the population formulas. Compare A and B, and what do you observe? Problem A Problem B Problem. A Oil (barrel) Odds Problem. B Oil (barrel) · Odds 2 25% · 2 · 25% 4 25% · 4 · 25% 4 25% · 4 · 25% 2 25% · 6 · 25%
part 3 4 The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5-minute period, Find the expected value and standard deviation. What is the probability that 2 customers will arrive in a 5-minute period? What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?
2. A department store receives an average of 5 returned items per day. The probability that a returned item has an available replacement is 0.65. [Hint: there are two separate distributions here.] d. e. f. Calculate the probability that there are 4 returned items and none has available replacements in a certain day. Calculate the variance and the mean of the returned items. Calculate the variance and the mean of the replaced items. 2
For a hypothesis test of a single population mean with unknown population standard deviation (σ�), we can use either Geogebra or Minitab. In Geogebra: use the “Statistics” tab in the Probability Calculator. Click the drop-down menu near the top (default is “Z Test of a Mean”) and choose “T Test of a Mean.” In Minitab: Select Stat > Basic Statistics > 1 sample t. Select Summarized Data from the drop-down menu. Check mark “Perform Hypothesis Test” and enter the hypothesized value. Click Options and select the appropriate alternate hypothesis. For both: Enter the sample mean, sample standard deviation, and sample size. We’ll use a sample with x¯=73.2�¯=73.2, s=14.16�=14.16, n=16�=16. For a hypothesis test of H0:μ=70 versus HA:μ>70�0:�=70 versus ��:�>70: The given sample has a test statistic of equation editor Equation Editor . The P-value for the test is equation editor Equation Editor . For a hypothesis test of H0:μ=75 versus HA:μ<75�0:�=75 versus…