A case−control study was performed among 145 subjects with macular degeneration and 34 controls, all of whom were 70- to 79-year-old women. A genetic risk score was developed to help differentiate the cases from the controls. The risk score was categorized into six groups (1, 2, 3, 4, 5, 6), with 6 being the highest risk and 1 being the lowest risk.The data in Table 10.48 were obtained relating the risk score to case/control status. taBlE 10.48 risk score cases controls 1 3 11 2 7 3 3 6 6 4 10 8 5 11 2 6 108 4 total 145 34 10.139 What test can be performed to study the asso- ciation between case/control status and risk score? Spe- cifically, we are interested in testing whether cases tend to have consistently higher risk scores or consistently lower risk scores than controls.

An owner of an ice cream shop wants to investigate whether a new training program affects the scooping skills of ice cream shop employees. To assess this, the owner divides employees into two groups: those who receive training (CT) and those who do not (NT). The owner evaluates their scooping skills using a scooping proficiency test. The dataset includes the test scores of the NT (no training) group: 15.00, 7.00, 18.00, 10.00, 6.00, and 20.00, and the CT (trained) group: 15.00, 10.00, 14.00, 7.00, 21.00, and 21.00. The owner is aware of the known population mean for scooping proficiency, which is 20. The hypothesis is that employees who did not receive training (NT) will likely have lower scooping proficiency than the population mean. To investigate this hypothesis, the owner conducts a one-sample t-test with a significance level (alpha) set at 0.05. The objective is to determine if the mean scooping proficiency of the NT group is significantly different from the established population…

A Michigan study concerning preference for outdoor activities used a questionnaire with a six-point Likert-type response in which 1 designated "not important" and 6 designated "extremely important." A random sample of n1 = 44 adults were asked about fishing as an outdoor activity. The mean response was x1 = 4.9. Another random sample of n2 = 49 adults were asked about camping as an outdoor activity. For this group, the mean response was x2 = 4.1. From previous studies, it is known that ?1 = 1.5 and ?2 = 2.0. Does this indicate a difference (either way) regarding preference for camping versus preference for fishing as an outdoor activity? Use a 5% level of significance. Note: A Likert scale usually has to do with approval of or agreement with a statement in a questionnaire. For example, respondents are asked to indicate whether they "strongly agree," "agree," "disagree," or "strongly disagree" with the statement.

During the summer of 2003, a nursing home measured the quality of administering medications to the residents.  Quality was divided into three categories: excellent – medication received within 15 minutes of scheduled time; acceptable – medication received between 15 and 30 minutes of scheduled time; and poor – medication received within 30 minutes of scheduled time.  The nursing home has set a quality standard that at least 75% of all medications should be of excellent quality.  A sample of 200 medication administrations resulted in 138 classified as excellent, 41 as acceptable, and 21 as poor.  In estimating the actual percentage of medications that are of excellent quality using a 90% confidence interval, we find:   a. (0.636, 0.744).   b. (0.625, 0.755).   c. (0.688, 0.692).   d. (0.639, 0.741).   e. there is insufficient information provided.