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A pharmaceutical company has designed a new test to identify marijuana users. It now wishes to assess the accuracy of this test. The company designed...

1.A pharmaceutical company has designed a new test to identify marijuana users. It now wishes to assess the accuracy of this test. The company designed an experiment with a total of 1000 individuals. 400 of them smoked marijuana before the test while 600 did not smoke. The test results are given in Table 2.

a) In this experiment what is the probability of testing negative for marijuana?

b) What is the probability of testing positive?

c) Given that a person tests positive, what is the probability that the person actually did smoke marijuana before the test?

2.Dr. Cluck's is a fried chicken chain with 100s of franchises around the country. A researcher would like to determine the average level of sales for its franchises last year. She chooses 16 franchises at random and based on this sample finds a mean of $2,780,000 with a standard deviation of $172,000. Calculate the following confidence intervals:

a) 90%

b) 95%

c) 99%

3.From the sample space S = {13, 94, 25, 72, 88}, what is the probability of getting an odd number?

4.If you have a sample mean of 72, which of the following intervals can you be the most confident that the true mean will fall in?

a) [66.64, 77.6]

b) [69.90, 74.10]

c) [70.60, 73.40]

5.Genevieve is studying the proliferation of extremely small dogs among the beautiful people of Los Angeles. Over one week she samples 100 outdoor restaurants, cafes and bars and counts the number of tiny pooches in each. Much to her chagrin, she finds that the little rascals are not as prevalent as she had initially assumed. In fact, this phenomenon is so rare, that there are no dogs in most establishments, a few establishments had one dog, and on rare occasions there would be multiple canines in one location. What type of distribution should Genevieve use to model her data?

6.Which distribution is the best to use when we have no prior knowledge of how the variable we are working with is distributed?

7.When we conduct hypothesis tests, we might encounter Type I or Type II error. Recall that Type I error occurs when we reject the null hypothesis when we should accept it, and Type II error occurs when we accept the null hypothesis when we should reject it. Are we controlling for Type I or Type II error when we say that our result is 'significant at the α= 0.05 level'?

8.What is the name of the company (or the product) William Gossest was working for when he developed Student's t-distribution?

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