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 121 random numbers gives outcomes with mean x¯ = 0.4364. Assume that the population remains fixed. We want to test

H0:=0.5
Ha:0.5

(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?

(2 points) 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 121 random numbers gives outcomes with mean x-0.4364. Assume that the population remains fixed. We want to test Ho: = 0.5 Ha: + 0.5 (a) Calculate the value of the z test statistic (b) Use Table C: is z significant at the 40% level ( = 0.4)? (Answer with "Yes/Y11 or "No/N.) (c) Use Table C: is z significant at the 0.1 % level ( = 0.001)? (Answer with "YesN" 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) -2.423 (b) Y (c) N (d) z: between 1.96 P-value: between 0.01 and -2.58 and 0.05

Explanation / Answer

d) As this is a two tailed test, and the z test statistic value is -2.423

The p-value is computed to be:

p= 2P(Z < -2.423 ) = 2*0.0077 = 0.0154

This p-value lies between 0.01 and 0.025

Therefoe the p-value lies between 0.01 and 0.025.

Now from the standard normal tables, we get:

P( -2.576 < Z < 2.576 ) = 0.01

P( - 2.241 < Z < 2.241 ) = 0.025

Therefore z lies between -2.576 and -2.241

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