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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Concept explainers

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!

Question

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
8.
60 up to 70
70 up to 80
80 up to 90
90 up to 100
109
682
1,757
1,694
100 up to 110
110 up to 120
649
94
120 or more
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.
O Ho: Random numbers are normally distributed with a mean of 90 and a standard deviation of 1O. HA: Random numbers are not
normally distributed with a mean of 90 and a standard deviation of 10.
O Ho: Random numbers are not normally distributed with a mean of 90 and a standard deviation of 10. HA: Random numbers are
normally distributed with a mean of 90 and a standard deviation of 10.
IN
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b-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3
decimal places.)
Test statistic
b-2. Fine the p-value?
O p-value <0.01
O 0.01B p-value <0.025
O 0.025 B pvalue< 0.05
O 0.05 3 p-value <0.10
O p-value 2o.10
c-1. What is the conclusion to the test?
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