Question

You are conducting a study to see if the accuracy rate for fingerprint identification is significantly different from 0.4. You use a significance level of
α=0.02
H0: p=0.4
H1: p≠0.4
You obtain a sample of size
n=298 in which there are 136 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 answers accurate to four decimal places.)
p-value =

Answer 1

Answer:

a)

Calculated Z -value = 2 < 2.326 at 0.02 level of significance

Null hypothesis is accepted

The accuracy rate for fingerprint identification is not significantly different from 0.4.  

b)

P-value of this sample = 0.0455

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 298

Sample proportion

                            $p^{-} = \frac{x}{n} = \frac{136}{298} = 0.456$

Population proportion

                          p = 0.4

Null hypothesis :-

The accuracy rate for fingerprint identification is not significantly different from 0.4

H₀: p=0.4

Alternative Hypothesis :-

The accuracy rate for fingerprint identification is  significantly different from 0.4

H₁: p≠0.4

Step(ii):-

Test statistic

               $Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }$

             $Z = \frac{0.456-0.4}{\sqrt{\frac{0.4 X 0.6}{298} } }$

             Z = 2

Given level of significance α=0.02

critical value Z = 2.326

Calculated Z -value = 2 < 2.326 at 0.02 level of significance

Null hypothesis is accepted

The accuracy rate for fingerprint identification is not significantly different from 0.4.  

P- value

P( Z>2) = 1- P( Z <2)

             = 1 - ( 0.5 - A(2)

            = 0.5 - 0.4772

           = 0.0228

Given two tailed test   = 2 ×P( Z >2)

                                      = 2 ×  0.0228

                                     = 0.0456

The p-value is 0.0456