H0 :=0.5 Ha :0.5 (d) Between which two Normal critical values z in the bottom ro
ID: 3363411 • Letter: H
Question
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 populatiorn 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 (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/Y" or "No/N".) (c) Use Table C: is z significant at the 0.1 % level ( = 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) -2.423 (b) Y (c) N (d) z: between and 2.576 P-value: between 0.01 (e) Y and 0.02Explanation / Answer
Here, we are already given that the p-value lies between 0.01 and 0.02, therefore the z value for these 2 p-values are computed as:
From the standard normal tables, we get:
P( Z < 2.326 ) = 0.99
Therefore, due to symmetry, we get:
P( -2.326 < Z < 2.326 ) = 0.98
Therefore the z value for p = 0.02 is 2.326
Also from the standard normal tables we get:
P( Z < 2.576 ) = 0.995
Therefore due to symmetry, we get:
P( -2.576 < Z < 2.576 ) = 0.99
Therefore for p = 0.01, the z value is 2.576
Therefore Z lies between 2.326 and 2.576
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