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7nadin3 [17]
3 years ago
5

You apply for a job and have to take a drug test. You are curious about the error rate for the test so you do some research. You

find a study where 47 out of 382 test results using this test were wrong (either a false positive or a false negative). The company that produces the drug test claims that less than 14% of the test results are wrong. Test if this seems accurate.
Mathematics
1 answer:
Ber [7]3 years ago
4 0

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

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} } }

         Z = \frac{0.1230-0.14}{\sqrt{\frac{0.14 X0.86}{382} } }

       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

               

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