Question

A die is tossed 600 times. H0 is the hypothesis that the proportion of tosses showing aces is binomially distributed with mean 1/6. Find the upper limit of the region for which H0 is accepted at the 1% level of significance in a two sided test.

A. .240

B. .243

C. .206

D. .252

E. .258

Answer 1

Solution:

Given:

n = a die is tossed = 600

p = the proportion of tosses showing aces is binomially distributed with mean = 1/6.

We have to find the upper limit of the region for which H0 is accepted at the 1% level of significance in a two sided test.

Upper limit is given by:

is z critical value for area.

Since we have to find z value for upper limit, so find area = 1 - 0.0050 = 0.9950

Thus look in z table for Area = 0.9950 or its closest area and find corresponding z critical value.

From above table we can see area 0.9950 is in between 0.9949 and 0.9951 and both are at same distance from 0.9950, Hence corresponding z values are 2.57 and 2.58

Thus average of both z values is 2.575

Thus   = 2.575

Thus

Thus correct answer is:  C. .206