please show the steps on how to solve it.

Step 1

Given that

X=16 , n=500

Step 2

p^=X/n=16/500=0.032

Null and alternative hypothesis

H0 : p = 0.04

H1 : p 0.04

Critical value:

The critical value for ?= 0.05 and for one tailed test.

Zc= 1.96

Test statistic ( z )

z = (p^ - p )/(p(1 - p)/n))

= ( 0.032 - 0.04 )/(0.04(1 - 0.04)/500))

= -0.913

P-value = 0.3613, at ?= 0.05 , z = -0.913 and for one tailed test.

Decision:-

P-value = 0.3613 > ?= 0.05 so does not reject the null hypothesis H0

1. When analyzing the accuracy of a machine classifier for cancer tissues, 16 of the 500 random samples were mis-classified. Use the data to test the hypotheses at 5% level of significance.

H0: p = 0.04

H1: p 0.04

Use the P-value method & show all computations and relevant information (test statistics, critical value, degree of freedom, etc.)

1. In Ques #1, determine the probability of the following error:

Pr ( mis-classification error is below 3%,

when the mis-classification error is 4% )