Testing a random number generator. A random number generator is supposed to prod
ID: 3153053 • Letter: T
Question
Testing a random number generator. A random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1. If this is true, the numbers generated come from a population with mu = 0.5 and sigma = 0.2887. A command to generate 100 random numbers gives outcomes with mean x^overbar = 0.4365. Assume that the population it remains fixed. We want to test H_0: mu = 0.5 H_a: mu NotEqual 0.5 Calculate the value of the z test statistic. Use Table C: is z significant at the 5% level (a = 0.05)? Use Table C: is z significant at the 1% level (a = 0.01)? Between which two Normal critical values z* in the bottom row of Table C does z lie. Between what two numbers does the P-value lie? Does the test give good evidence against the null hypothesis?Explanation / Answer
A)
Formulating the null and alternative hypotheses,
Ho: u = 0.5
Ha: u =/ 0.5
As we can see, this is a two tailed test.
Getting the test statistic, as
X = sample mean = 0.4365
uo = hypothesized mean = 0.5
n = sample size = 100
s = standard deviation = 0.2887
Thus, z = (X - uo) * sqrt(n) / s = -2.199515068 = -2.20 [ANSWER]
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b)
As for alpha = 0.05 two tailed,
zcrit = +/- 1.96
then as |Z| > 1.96, YES, IT IS SIGNIFICANT. [ANSWER]
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c)
As for alpha = 0.01 two tailed,
zcrit = +/- 2.58
then as |Z| < 2.58, NO, IT IS NOT SIGNIFICANT. [ANSWER]
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d)
It lies between 1.96 and 2.33.
Hence, 0.02 < P < 0.05.
As this is a small P value at 0.05 level, yes, it gives good evidence against the null hypothesis.
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