The paper "Breast MRI as an Adjunct to Mammography for Breast Cancer Screening in High-Risk Patients" describes a study that investigated the usefulness of MRI (magnetic resonance imaging) to diagnose breast cancer. MRI exams from 650 women were reviewed. Of the 650 women, 13 had breast cancer, and the MRI exam detected breast cancer in 12 of these women. Of the 637 women who did not have breast cancer, the MRI correctly identified that no cancer was present for 547 of them. The accompanying table summarizes this information. †   Breast Cancer Present Breast Cancer Not Present Total MRI Indicated Breast Cancer 12 90 102 MRI Did Not Indicate Breast Cancer 1 547 548 Total 13 637 650   a.    Use the information in the table to approximate the probability of this type of error. (Hint: See Example 10.8. Enter your probability as a decimal)   b.   Use the information in the table to approximate the probability of this type of error. (Enter your probability as a decimal )

Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a​ brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that​ "blue enhances performance on a creative​ task." Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b). background u n x s   Blue μ1 36 4.38 0.55 Red μ2 41 3.79 0.84 The test​ statistic, t, is enter your response here. ​(Round to two decimal places as​ needed.) The​ P-value is enter your response here. ​(Round to three decimal places as​ needed.) b. Construct the confidence…

In an article entitled “Bucket-Handle Meniscal Tears of the Knee: Sensitivity and Specificity of MRI signs,” Dorsay and Helms (A-6) performed a retrospective study of 71 knees scanned by MRI. One of the indicators they examined was the absence of the “bow-tie sign” in the MRI as evidence of a bucket-handle or “bucket-handle type” tear of the meniscus. In the study, surgery confirmed that 43 of the 71 cases were bucket-handle tears. The cases may be cross-classified by “bow-tie sign” status and surgical results as follows:     Tear Surgically Confirmed Tear Surgically Confirmed As Not Present Total Positive Test (absent bow-tie sign)               38                10             48 Negative Test (bow-tie sign presence)                 5                18             23     Total                   43              28             71     Source: Theodore A. Dorsay and Clyde A. Helms, “Bucket-handle Meniscal Tears of the Knee: Sensitivity and…

Suppose that 73.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 1000 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 718 suffered from hypertension. The researchers want to use a one‑sample ?z‑test for a population proportion to see if the proportion of type 2 diabetics who have hypertension while taking their new drug, ?p, is different from the proportion of all type 2 diabetics who have hypertension. They decide to use a significance level of ?=0.01α=0.01. Determine the value of the ?z‑test statistic. Give your answer precise to two decimal places. Determine the ?-valueP-value for this test. Give your answer precise to three decimal places.