Answer:
A)
<u><em>Null hypothesis:H₀:-</em></u><em> There is no significant difference between in drug resistance between the two states</em>
<u><em>Alternative Hypothesis :H₁:</em></u>
<em>There is significant difference between in drug resistance between the two states</em>
<em>B)</em>
<em>The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance</em>
<em> Rejected H₀</em>
<em>There is a significant difference in drug resistance between the two states.</em>
C)
P - value = 0.0066
<em>P - value = 0.0066 < 0.02</em>
<em>D) </em>
<em>1) Reject H₀ </em>
<em>There is a significant difference in drug resistance between the two states.</em>
Step-by-step explanation:
<u><em>Step(i):-</em></u>
<em>Given first sample size n₁ = 174</em>
Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant.
<em>First sample proportion </em>
<em>Given second sample size n₂ = 375</em>
Given data Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant
<em>Second sample proportion</em>
<em> </em><em></em>
<u><em>Step(ii):-</em></u>
<u><em>Null hypothesis:H₀:-</em></u><em> There is no significant difference between in drug resistance between the two states</em>
<u><em>Alternative Hypothesis :H₁:</em></u>
<em>There is significant difference between in drug resistance between the two states</em>
<em>Test statistic</em>
<em> </em><em></em>
<em> Where </em>
<em> </em><em></em>
<em> </em><em></em>
<em> Q = 1 - P = 1 - 0.0327 = 0.9673</em>
<u><em>Step(iii):-</em></u>
<em></em>
<em> Test statistic</em>
<em> </em><em></em>
<em> </em><em></em>
<em> Z = 2.7261</em>
<em> </em>
<em>Level of significance = 0.02 or 0.98</em>
<em>The z-value = 2.054</em>
<em>The calculated value Z = 2.7261 > 2.054 at 0.02 level of significance</em>
<em> Reject H₀ </em>
<em>There is a significant difference in drug resistance between the two states.</em>
<u><em>P- value </em></u>
<em>P( Z > 2.7261) = 1 - P( Z < 2.726)</em>
<em> = 1 - ( 0.5 + A (2.72))</em>
<em> = 0.5 - 0.4967</em>
<em> = 0.0033</em>
we will use two tailed test
<em>2 P( Z > 2.7261) = 2 × 0.0033</em>
<em> = 0.0066</em>
<em>P - value = 0.0066 < 0.02</em>
<em> Reject H₀ </em>
<em>There is a significant difference in drug resistance between the two states.</em>