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barxatty [35]
3 years ago
6

A test for marijuana usage was tried on 170 subjects who did not use marijuana. The test result was wrong 8 times.a. Based on th

e available​ results, find the probability of a wrong test result for a person who does not use marijuana.b. Is it​ "unlikely" for the test to be wrong for those not using​ marijuana? Consider an event to be unlikely if its probability is less than or equal to 0.05.
Mathematics
1 answer:
motikmotik3 years ago
6 0

Answer:

a. 0.047

b. Unlikely.

Step-by-step explanation:

a. The probability of a test result being wrong for a person not using mrijuana  = 8 / 170 = 0.047.

b. As the probability for a wrong result is < 0.05 we can say that the test is unlikely to be wrong.

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Answer:

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Step-by-step explanation:

Data given and notation  

\bar X=3.1 represent the sample mean

\sigma=\sqrt{6} represent the sample standard deviation for the sample

n=47 sample size  

\mu_o =3 represent the value that we want to test

\alpha represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is higher than 3, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3  

Alternative hypothesis:\mu > 3  

If we analyze the size for the sample is > 30 and we know the population deviation so is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic

We can replace in formula (1) the info given like this:  

z=\frac{3.1-3}{\frac{2.449}{\sqrt{47}}}=0.280    

P-value

Since is a one side test the p value would be:  

p_v =P(z>0.280)=0.390  

Conclusion  

If we compare the p value and the significance level assumed \alpha=0.01 we see that p_v>\alpha so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the height of men actually its NOT significant higher than 0.3 at 1% of signficance.  

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