A random number generator is supposed to produce random numbers that are uniform

Question

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 0.5 and 0.2887 . A command to generate 100 random numbers gives outcomes with mean x-0.4365 . Assume that the population remains fixed, we want to test Ho : = 0.5 and Ha : 0.5 4 points) Calculate the value of the z test statistic. (3 points) Is z statistically significant at the 5% level ( = 0.05), show your work? (3 points) Is z statistically significant at the 1% level (-0.01), show your work? (5 points) If 2.054

Explanation / Answer

1)here std error of mean =std deviation/(n)1/2 =0.2887/(100)1/2 =0.02887

hence test statistic z =(X-mean)/std error =(0.4365-0.5)/0.02887=-2.1995

2) for 0.05 level ; critical value of z are -/+ 1.96

as test statistic is in critical region therefore test is statistically significant.

3)

for 0.01 level ; critical value of z are -/+ 2.5758

as test statistic is not in critical region therefore test is not statistically significant.

4) for 2.054 and 2.326 are critical values for 0.02 and 0.04 level of significance ; tehrefore test statistic lie between

0.02 and 0.04 p values.

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