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 frequency distribution shown below. The sample mean and sample standard deviation are 100 and 10, respectively?

Value ............................... Frequency

Under 70 ................................. 12

70 up to 80 ............................... 99

80 up to 90 ............................. 658

90 up to 100 .......................... 1734

100 up to 110 ......................... 1681

110 up to 120 ........................... 697

120 up to 130 .......................... 112

130 or more ............................... 7

.................................... 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.

b. What is the critical value at the 1% significance level?

c. Calculate the value of the test statistic.

d. What is the conclusion to the test? Is your conclusion sensitive within the range of typical significance levels?