Is it 0.05)? Is it statistically s random number generator 1718 Testing a Random

Question

Is it 0.05)? Is it statistically s random number generator 1718 Testing a Random Number Generator. A on is supposed to produce random numbers that are uniformly distributed the interval from 0 to 1. If this is true, the numbers generated come from a population with Au 0.5 and o 0.2887. A command to generate 100 random numbers gives outcomes with mean X 0.4365. Assume that the population or remains fixed. We want to test 0.5 Ho: Ha: Au 0.5 (a) Calculate the value of the z test statistic. (b) Use Table C: is z statistically significant at the 5% level (a 0.05)? (c) Use Table C: is z statistically significant at the 1% level (a 0.01)? (d) 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

Given in the question

Mean = 0.5 sd=0.2887

Xbar= 0.4365

Z= 0.4365-0.5 / 0.2887

Z=- 0.0635/0.2887

Z =- 0.211951

This is two tail test

So P-value at z=-0.211951 and alpha =0.05 is 0.83288 which is greater than 0.05 so this is not significant.

P-value at z=-0.211951 and alpha=0.01 is 0.83 which is greater than 0.01 so this is also not significant.

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