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german
3 years ago
5

Each year, more than 2 million people in the United States become infected with bacteria that are resistant to antibiotics. In p

articular, the Centers of Disease Control and Prevention have launched studies of drug-resistant gonorrhea.† Suppose that, of 174 cases tested in a certain state, 11 were found to be drug-resistant. Suppose also that, of 375 cases tested in another state, 7 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a 0.02 level of significance. (Let p1 = the population proportion of drug-resistant cases in the first state, and let p2 = the population proportion of drug resistant cases in the second state).
A. State the null and alternative hypotheses.
B. Find the value of the test statistic.
C. What is the p-value?
D. What is your conclusion?
1. Reject H0. There is a significant difference in drug resistance between the two states.
2. Do not reject H0. There is a significant difference in drug resistance between the two states.
3. Reject H0. There is not a significant difference in drug resistance between the two states.
4. Do not reject H0. There is not a significant difference in drug resistance between the two states.
Mathematics
1 answer:
Bingel [31]3 years ago
8 0

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>

                    p_{1} = \frac{x_{1} }{n_{1} } = \frac{11}{174} = 0.0632

<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>p_{2} = \frac{x_{2} }{n_{2} } = \frac{7}{375} = 0.0186<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>Z = \frac{p_{1}-p_{2}  }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }<em></em>

<em>        Where </em>

<em>         </em>P = \frac{n_{1}p_{1} +n_{2} p_{2}  }{n_{1} +n_{2} }<em></em>

<em>        </em>P = \frac{174 (0.0632) + 375 (0.0186) }{174+375 } =  \frac{17.9718}{549} = 0.0327<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>Z = \frac{p_{1}-p_{2}  }{\sqrt{PQ(\frac{1}{n_{1} }+\frac{1}{n_{2} } ) } }<em></em>

<em>          </em>Z = \frac{0.0632-0.0186  }{\sqrt{0.0327 X 0.9673(\frac{1}{174 }+\frac{1}{375 } ) } }<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>

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