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 mu = 0.5 and sigma = 0.2887. A command to generate 144 random numbers gives outcomes with mean bar x = 0.4363. Assume that the population sigma remains fixed. We want to test H_0: mu = 0.5 H_a: mu notequalto 0.5 (a) Calculate the value of the z test statistic. (b) Use Table C: is z significant at the 40% level (alpha = 0.4)? (Answer with "Yes/Y" or "No/N".) (c) Use Table C: is z significant at the 0.1% level (alpha = 0.001)? (Answer with "Yes/Y" or "No/N".) (d) Between which two Normal critical values z* in the bottom row of Table C does the absolute value of z 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) z: between and P-value: between and (e)

Explanation / Answer

Solution:-

zcritical for at significance 0.4 are 0.84, z has to lie between - 0.84 and 0.84

alpha/2 = 0.2

1-(alpha/2) = 0.8

Limits for p value = (0.2, 0.8)

z critical = 0.84

0.84 < z < 0.84

zcritical for at significance 0.001 are 3.29, z has to lie between - 3.29 and 3.29

alpha/2 = 0.0005

1-(alpha/2) = 0.9995

Limits for p value = (0.0005, 0.9995)

z critical = 3.29

- 3.29 < z < 3.29

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