O According to a 2018 article in Esquire magazine, approximately 70% of males over age 70 will develop cancerous cells in their prostate. Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of the most common tests for the detection of prostate cancer is the prostate-specific antigen (PSA) test. However, this test is known to have a high false-positive rate (tests that come back positive for cancer when D no cancer is present). Suppose there is a 0.02 probability that a male patient has prostate cancer before testing. The probability of a false-positive test is 0.75, and the probability of a false-negative (no indication of cancer when cancer is actually present) is 0.20. Let C = event male patient has prostate cancer += positive PSA test for prostate cancer - = negative PSA test for prostate cancer a. What is the probability that the male patient has prostate cancer if the PSA test comes back positive (to 4 decimals)? b. What is the probability that the male patient has prostate cancer if the PSA test comes back negative (to 4 decimals)? c. For older men, the prior probability of having cancer increases. Suppose that the prior probability of the male patient is 0.3 rather than 0.02. What is the probability that the male patient has prostate cancer if the PSA test comes back positive (to 4 decimals)? What is the probability that the male patient has prostate cancer if the PSA test comes back negative (to 4 decimals)? d. What can you infer about the PSA test from the results of parts (a), (b), and (c)? The difference between P(C|+) and P(C|-) in parts (a) and (b) is Select your answer v than the difference between P(C+) and P(C|-) in part (c).

An article published in the “American Journal of Public Health” describes the results of a health survey administered to 119 male convicts, 50 years of age or older, residing in a state social rehabilitation center. It was found that 21.6% of them claimed to have a history of venereal diseases. Based on these findings, we wish to evaluate whether more than 15% of this population has a history of venereal diseases. What would be the p value that allows evaluating the research question? A. 4.32 B. 2.09 C. -1.72 D. 0.018 E. 0.957

Radio frequency identification​ (RFID) is an electronic scanning technology that can be used to identify items in a number of ways. One advantage of RFID is that it can eliminate the need to manually count​ inventory, which can help improve inventory management. The technology is not​ infallible, however, and sometimes errors occur when items are scanned. The probability that a scanning error occurs is 0.0069. 1. Find the probability that the number of items scanned incorrectly is between 16 and 20 ​, ​inclusive, from the next 5100 items scanned. *Kindly explain the procedure in Excel for this* A) The probability is (Round to four decimal places as​ needed.) 2. Find the expected number of items incorrectly from the next 5100 items B) The probability is (Round to four decimal places as​ needed.)

A large company that produces a "tat-burner pill claims an average Ioss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group Would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds. Let the standard deviation of the population be 7.5 pounds. Clearly state the hypotheses, obtain the test statistic and p-value, and state the decision and conclusion. Show all your work.

The state highway department is studying traffic patterns on one of the busiest highways in the state. As part of the study. the department needs to estimate the average number of vehicles that pass an intersection each day. One of the department's officer (Officer A) claims that on average, more than 15,000 cars passing the intersection. On the other hand. Officer B claims that on average, 18,000 cars passing the intersection. Meanwhile, a random sample of 64 days gives a sample mean of 14,205 cars and a sample standard deviation of 1,010 cars. Test both claim at 0.05 level of significance. Use the critical value approach and show the complete calculation steps for each testing. Whose claim is true? Testing Officer A's claim Step 1: State the hypotheses Step 2: Find critical value and state the decision rule Step 3: Compute the test value Step 4: Make decision Step 5: Conclusion Testing Officer B's claim Step 1: State the hypotheses Step 2: Find critical value and state the decision…

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Predict whether they are cause-effect, accidental, or common-cause. Explain your conclusion and, if they are cause-effect, explain which causes the other and why. "People who drink more coffee in the morning are more likely to have insomnia (the inability to sleep) at night."