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:
Step(i):-
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
[tex]p = \frac{x}{n} = \frac{47}{382} = 0.1230[/tex]
Null hypothesis: H₀ : P = 0.14
Alternative Hypothesis:H₁ : P≠ 0.14
Step(ii):-
Test statistic
[tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]
[tex]Z = \frac{0.1230-0.14}{\sqrt{\frac{0.14 X0.86}{382} } }[/tex]
Z = - 1.0
|Z| = |-1.0| < 1.96 at 0.05 level of significance.
Final answer:-
The null hypothesis is accepted
The company that produces the drug test claims that less than 14% of the test results are wrong
