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

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

Explanation:

Step(i):-

Given sample size 'n' = 298

Sample proportion

`p^(-) = (x)/(n) = (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{(P Q)/(n) } }`

`Z = \frac{0.456-0.4}{\sqrt{(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