Question

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly more than 0.85. You use a significance level of ?=0.002.

      H0:p=0.85
      H1:p>0.85

You obtain a sample of size n=147 in which there are 128 successes.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

less than (or equal to) ??

greater than ??

This test statistic leads to a decision to...

reject the null

accept the null

fail to reject the null

As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is more than 0.85.

There is not sufficient evidence to warrant rejection of the claim that the accuracy rate for fingerprint identification is more than 0.85.

The sample data support the claim that the accuracy rate for fingerprint identification is more than 0.85.

There is not sufficient sample evidence to support the claim that the accuracy rate for fingerprint identification is more than 0.85.

Answer 1

H0:p=0.85
      H1:p>0.85
alpha = 0.002
sample of size n=147

there are x=128 successes.
p = x/n = 128/147 = 0.8707

test statistic =

Z = ( p - P ) / sqrt ((P*(1-P)) ÷ n )

= ( 0.8707 - 0.85 ) / sqrt ((0.85*(1-0.85))÷147)

Z = 0.705

Zcritical = 2.88

p-value = P ( Zalpha > 0.705 ) = 0.2406 > 0.002 = alpha

The p-value is 0.2406 greater than alpha

This test statistic leads to a decision to

fail to reject the null

There is not sufficient sample evidence to support the claim that the accuracy rate for fingerprint identification is more than 0.85.