Is 8:12 equivalent to 10:15
2 answers:
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Answer:
a)
<em>Calculated Z -value = 2 < 2.326 at 0.02 level of significance</em>
<em>Null hypothesis is accepted</em>
<em>The accuracy rate for fingerprint identification is not significantly different from 0.4. </em>
<em>b)</em>
<em>P-value of this sample = 0.0455</em>
<em></em>
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given sample size 'n' = 298
<em>Sample proportion </em>
<em> </em><em></em>
<em>Population proportion </em>
p = 0.4
<u><em>Null hypothesis</em></u> :-
<em>The accuracy rate for fingerprint identification is not significantly different from 0.4</em>
<em>H₀: p=0.4</em>
<u><em>Alternative Hypothesis :-</em></u>
<em>The accuracy rate for fingerprint identification is significantly different from 0.4</em>
<em>H₁: p≠0.4</em>
<u><em>Step(ii):</em></u>-
<em>Test statistic</em>
Z = 2
<em>Given level of significance α=0.02</em>
<em>critical value Z = 2.326</em>
<em>Calculated Z -value = 2 < 2.326 at 0.02 level of significance</em>
<em>Null hypothesis is accepted</em>
<em>The accuracy rate for fingerprint identification is not significantly different from 0.4. </em>
<u><em> P- value </em></u>
<em>P( Z>2) = 1- P( Z <2)</em>
<em> = 1 - ( 0.5 - A(2)</em>
<em> = 0.5 - 0.4772</em>
<em> = 0.0228</em>
<em>Given two tailed test = 2 ×P( Z >2)</em>
<em> = 2 × 0.0228</em>
<em> = 0.0456</em>
<em>The p-value is 0.0456</em>