Mammography and clinical breast examination are the two major techniques used to screen for breast cancer. However, as true for any screening test, they are not completely accurate. If it is determined, based on mammographic findings, that there is a possibility of breast cancer, this is usually confirmed or disconfirmed by a subsequent biopsy. A false positive test is a mammogram positive test that is disconfirmed by biopsy. The data in Table 1 were reported in a paper concerning breast cancer screening (Elmore, et al, New England Journal of Medicine 1998; 338(16): 1089-1096). Table 1 False positive breast cancer screening tests over a 10-year period # Screening tests # False positive tests 9762 631 1. Another aspect of mammographic screening is the presence of false negatives. A false negative is a screen negative woman who has breast cancer. False negatives usually occur because the tumors are small and hard to detect. It is estimated that among women with breast cancer, 2% of all screening tests are false negatives. Suppose that there are 100 women who have breast cancer. What is the probability that at least 3 of them will not be detected by a mammogram?

Using the latest in medical technology, an orthopedic doctor has developed a new surgical procedure that he believes is an improvement over the standard procedure. He wants to study whether the mean recovery time of patients who have the new procedure is less than the mean recovery time of patients who have the standard procedure. The doctor studies a random sample of 11 patients who have the new procedure and a random sample of 10 patients who have the standard procedure. (These samples are chosen independently.) The doctor records each patient's recovery time (in days). These data are shown in the table. Recovery times (in days) 350, 284, 291, 393, 295, 377, 401, 371, 423, 449, 364 New procedure Standard procedure 435, 409, 419, 423, 388, 410, 412, 438, 396, 424 Send data to calculator Send data to Excel Assume that the two populations of recovery times are approximately normally distributed. Can the doctor conclude, at the 0.01 level of significance, that the population mean of the…

In the early 1970s, a young man challenged an Oklahoma state law that prohibited the sale of 3.2% beer to males under age 21 but allowed its sale to females in the same age group. The case (Craig v. Boren, 429 U.S. 190, 1976) was ultimately heard by the U.S. Supreme Court. The state of Oklahoma argued that the law improved traffic safety. One of the three main pieces of data presented to the court was the result of a “random roadside survey.” This survey gathered information on gender and whether or not the driver had been drinking alcohol in the previous 2 hours. A total of 619 drivers under 21 years of age were included in the survey. The chi-square test statistic is approximately 1.64 for this data. Find the P-value State a conclusion at a 5% level of significance. Do you think that the data supports the Oklahoma law that forbids sale of 3.2% beer to males and permits it to females? See image.

A researcher is studying the effects of his newly created lens on vision. He samples 9 people with poor vision and measures their visual distance (in feet) with the lens and then without the lens. Did people’s vision with the lens differ from their vision without?   Participant # With Lens Without Lens 1 8 14 2 6 17 3 9 12 4 7 11 5 5 12 6 9 18 7 8 13 8 9 7 9 7 13   What kind of analysis will you use? Why?  State the null and alternative hypothesis.    Check your assumptions. Explain why each of them are or are not met.    Sketch a distribution and shade the rejection region(s), including the corresponding critical value(s).    Using R, calculate your test statistic and interpret the results of your test. (Don’t forget your 95% confidence interval and screenshots of your work!)  What do you conclude about the null hypothesis? Are there significant differences?