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 μμ = 0.5 and σσ = 0.2887. A command to generate 169 random numbers gives outcomes with mean x¯¯¯x¯ = 0.4366. Assume that the population σσ remains fixed. We want to test

H0:μ=0.5

Ha:μ≠0.5

(a) Calculate the value of the Z test statistic.
(b) Use Table C: is z significant at the 40% level (αα = 0.4)? (Answer with "Yes/Y" or "No/N".)
(c) Use Table C: is z significant at the 0.1% level (αα = 0.001)? (Answer with "Yes/Y" or "No/N".)
(d) Between which two Normal critical values z∗z∗ in the bottom row of Table C does the absolute value of zz lie? Between what two numbers does the P - value lie?
(e) Does the test give good evidence against the null hypothesis? (Answer with "Yes/Y" or "No/N".)

(a)
(b)
(c)
(d) zz: between  and
P-value: between  and
(e)

Answer 1