Answer:
Test statistic Z = -1.0
|Z| = |-1.0| < 1.96 at 0.05 level of significance.
The null hypothesis is accepted
The company that produces the drug test claims that less than 14% of the test results are wrong
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the population proportion P = 14% =0.14
Given that the sample size 'n' = 382 tests
Given that find a study where 47 out of 382 test results using this test were wrong (either a false positive or a false negative).
Sample proportion
![p = \frac{x}{n} = \frac{47}{382} = 0.1230](https://tex.z-dn.net/?f=p%20%3D%20%5Cfrac%7Bx%7D%7Bn%7D%20%3D%20%5Cfrac%7B47%7D%7B382%7D%20%3D%200.1230)
Null hypothesis: H₀ : P = 0.14
Alternative Hypothesis:H₁ : P≠ 0.14
<u><em>Step(ii):-</em></u>
Test statistic
![Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7Bp-P%7D%7B%5Csqrt%7B%5Cfrac%7BPQ%7D%7Bn%7D%20%7D%20%7D)
![Z = \frac{0.1230-0.14}{\sqrt{\frac{0.14 X0.86}{382} } }](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B0.1230-0.14%7D%7B%5Csqrt%7B%5Cfrac%7B0.14%20X0.86%7D%7B382%7D%20%7D%20%7D)
Z = - 1.0
|Z| = |-1.0| < 1.96 at 0.05 level of significance.
<u><em>Final answer:-</em></u>
The null hypothesis is accepted
The company that produces the drug test claims that less than 14% of the test results are wrong