Question

please answer question and show all steps. thank you :)

Los Angeles & Marijuana Marijuana refers to the dried leaves, flowers, stems, and seeds from the Cannabis sativa or Cannabis indica plant. The plant contains the mind-altering chemical THC and other similar compounds. Marijuana is the most commonly used illicit drug in the United States. In Los Angeles, California, an industry with DISA Drug Test combines technology and screening innovations provides a "1-Panel-THC" test for marijuana usage in employee. Among 300 tested subjects, results from 27 subjects were wrong, so the result is either a

Answer 1

Claim: less than 10% of the results are wrong.

n = sample size = 300

x = number of wrong test result = 27

level of significance = 0.05

Let's write null and alternative hypothesis as

null hypothesis is H₀ : P= 0.10

and alternative hypothesis is H₁ : P < 0.1

We can used one sample proportion z test.

Using minitab.

The command for one sample proportion z test in minitab is

Stat>>>Basic statistics>>>1-proportion...

Then click on summarized data

number of events = x = 27

Number of trials = n = 300

Click on "Perform hypothesis test

Hypothesized proportion = P = 0.1 (because under the null hypothesis P = 0.1)

then click on option

Level of confidence in percentage = c = ( 1- $\alpha$)*100 = = (1 -0.05)*100 = 95.0

so put "Confidence level " = 95.0

Alternative = less than

then click on "Use test and interval based on normal approximation"

Then click on OK and again click on OK

So we get the following output

Test and Cl for One Proportion Test of p = 0.1 vs p < 0.1 Sample X 27 N 300 Sample p 0.090000 95% Upper Bound Z-Value 0.117177 -0.58 P-value 0.282 Using the normal approximation.

From the above output, we get

test statistic value , Z = -0.58

P-value = 0.282

Decision rule:

1) If p-value < level of significance (alpha) then we reject null hypothesis

2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.

Here p value = 0.282 > 0.05 so we used 2nd rule.

That is we fail to reject null hypothesis

Conclusion: At 5% level of significance there are not sufficient evidence to say that the sample data indicates less than 10% of the results are wrong.

So the test may no appear to be good for most purpose.