HYPOTHESIS TESTING AND TYPE ERRORS Free Essay Example, 1000 words

Write a paragraph explaining which error would be more severe, and why. In my opinion, Type II error would be more severe. This is because in this case people will not buy Drug B and hence will not avail better treatment for depression when it is in fact available. In case of Type I error, People will waste money buying Drug B, when the less expensive Drug A is just as effective in treatment for depression. However, when we choose between better treatment and money, we will always go for better treatment. 6. Cough-a-Lot children’s cough syrup is supposed to contain 6 ounces of medicine per bottle. However, since the filling machine is not always precise, there can be variation from bottle to bottle. The amounts in the bottles are normally distributed with ÏÆ' = 0.3 ounces. A quality assurance inspector measures 10 bottles and finds the following (in ounces): 5.95 6.10 5.98 6.01 6.25 5.85 5.91 6.05 5.88 5.91 Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle? a. State the hypothesis you will test. The null and alternate hypotheses tested are H0: ÃŽ ¼ = 6 H1: ÃŽ ¼ ≠  6 b. We will write a custom essay sample on HYPOTHESIS TESTING AND TYPE ERRORS or any topic specifically for you Only $17.96 $11.86/pageorder now Calculate the test statistic. Sample Mean, Since, the population standard deviation, ÏÆ' is known, the test will be One-Sample Z-Test for a population (hypothesized) mean. The test statistic is c. Find the P-value. The P-value is P-value (Two-tailed) = 2(0.4522) = 0.9044 d. What is the conclusion? Fail to reject H0, as the P-value = 0.9044 > 0.05. Thus, the results are not enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle. 7. Calculate a Z score when X = 20, ÃŽ ¼ = 17, and ÏÆ' = 3.4. 8. Using a standard normal probabilities table, interpret the results for the Z score in Problem 7. The area above Z-score of 0.88 in a standard normal probabilities table is 0.1894. Thus, there is a probability of 0.1894 that an X-score will be greater than 20. Alternatively, we can say that there is a probability of 0.8106 that an X-score will be less than 20. 9. Your babysitter claims that she is underpaid given the current market. Her hourly wage is $12 per hour. You do some research and discover that the average wage in your area is $14 per hour with a standard deviation of 1.9. Calculate the Z score and use the table to find the standard normal probability. Based on your findings, should you give her a raise? Explain your reasoning as to why or why not. The probability that the hourly wage of a babysitter is below $12 is about 0.1469 (14.69%).