Radiology, Cancer A radiologist investigates whether a new (less costly) method for identifying esophageal cancer is as effective as the gold standard. He obtains the following test results: false positive = 0, true positive = 46, false negative = 1, true negative = 17. (a) What is the sensitivity of the test? (Round your answer to four decimal places.) [09787] (b) Consider the following Excel spreadsheet. BINOMDIST(45, 47, p, TRUE) Р 0.8000 1.000 0.8100 0.999 0.8200 0.999 0.8300 0.998 0.8400 0.997 0.8500 0.996 0.8600 0.993 0.8700 0.988 0.8800 0.982 0.8900 0.972 0.9000 0.956 0.9100 0.933 0.9200 0.899 0.9300 0.850 0.9400 0.782 0.9500 0.688 0.9600 0.566 0.9700 0.414 0.9800 0.242 0.9900 0.080 0.9950 0.023 0.9990 0.001 0.9995 0.000 True positves True positive + False nego BINOMDIST(46, 47, p, TRUE) 1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.998 0.996 0.993 0.988 0.980 0.967 0.945 0.910 0.853 0.761 0.613 0.376 0.210 0.046 0.023 46 47 46+1 = 0.97872340 = 0.9787 Provide a 95% CI for the sensitivity. (Enter your answer using interval notation. Round your numerical values to two decimal places. Hint: The above Excel spreadsheet might be useful.)

A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM majors than Social Science and Liberal Arts major. He asked each of his 50 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly. -20 - STEM -20 - Social Sciences -10 - Liberal arts What is the variable in this test? What type of variable is it, and what are the null and alternative hypothesis?

If age were held fixed, but a person put on 15 pounds, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)If a person kept the same weight but got 15 years older, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)(e) Test each coefficient to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.)   t P value β2     β3

Analysis produced the following results: Total Sum of Squares 4633 Unexplained Sum of Squares 2010 What percentage of the variation in the dependent variable has been explained by variation in the independent variable?

You may need to use the appropriate appendix table or technology to answer this question. Of 290 female registered voters surveyed, 119 indicated they were planning to vote for the incumbent president. Of 425 male registered voters, 157 indicated they were planning to vote for the incumbent president. (a) Compute the test statistic. (Use female male. Round your answer to three decimal places.) (b) At a = 0.01, test to see if there is a significant difference between the population proportions of females and males who plan to vote for the incumbent president. (Use the p-value approach.) Calculate the p-value. (Round your answer to three decimal places.) p-value = What is your conclusion? O Do not reject Ho. We can conclude that there is a significant difference between the two poplation proportions. O Do not reject Ho. We cannot conclude that there is a significant difference between the two population proportions. O Reject Ho. We cannot conclude that there is a significant difference…

What is t critical for a study that contains 9 participants in one group and 11 is another group? Input three decimals. Answer:

The z-test Assume that a treatment does have an effect and that the treatment effect is being evaluated with a z hypothesis test. If all factors are held constant, how is the outcome of the hypothesis test influenced by sample size? To answer this question, do the following two tests and compare the results. For both tests, a sample is selected from a normal population distribution with a mean of u = 32 and a standard deviation of o = 11. After the treatment is administered to the individuals in the sample, the sample mean is found to be M = 35. In each case, use 10.1 a two-tailed test with a = .05. For the first test, assume that the sample consists of n = 16 individuals. For the second test, assume that the sample consists of n = 64 individuals. Explain in your own words how the outcome of the hypothesis test is influenced by the sample size. а. b. с. (Note: Be sure and show a full diagram of the research design. Also show all steps and calculations you made for each test following…

If age were held fixed, but a person put on 15 pounds, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)If a person kept the same weight but got 15 years older, what would you expect for the corresponding change in systolic blood pressure? (Use 2 decimal places.)(e) Test each coefficient to determine if it is zero or not zero. Use level of significance 5%. (Use 2 decimal places for t and 3 decimal places for the P-value.)   t P value β2     β3

A college in the northeastern United States used SAT scores to help decide which applicants to admit. To determine whether the SAT was useful in predicting success, the college examined the relationship between SAT scores and first – year GPAs of admitted students. Below is a table with the data collected.  (a) What would you predict the GPA to be for a student whose Math SAT score is 650? (b) What process of prediction did you use for part (a) ? Is this a good prediction? (c) What would you predict the GPA to be for a student whose Math SAT score is 725? (d) What process of prediction did you use for part (b)? Is this a good prediction? Math SAT Scores First – Year GPAs 509 2.6 471 2.3 700 2.4 719 3 710 3.1 643 2.9 665 3.1 719 3.3 693 2.3 701 3.3 614 2.6 557 3.3 611 2 701 3