1. A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. The mean wake time of 35 subjects using the drug was 95.4 min with a standard deviation of 21.6 min. Assume that the population is normally distributed. Construct a 95% confidence interval estimate of the mean.

2. A 2020 study was conducted to examine the relationship between COVID-19 and other infections among patients in intensive care units. The researchers found that of 472 patients diagnosed with COVID-19 and mechanically ventilated, 330 had a secondary respiratory infection. Construct a 90% confidence interval for the proportion of all mechanically ventilated COVID-19 patients that have secondary respiratory infections.

3. The objective of a randomized controlled trial was to determine whether providing women with additional information on the pros and cons of screening for cervical cancer would increase the willingness to be screened. A treatment group of 155 women received a leaflet on screening that contained more information (average individual risk for cervical cancer, likelihood of positive finding, the possibility of false positive/negative results, etc.) than the standard leaflet developed by the British National Health Service that 160 women in a control group received. In the treatment group, 120 women indicated they wanted to have the screening test for cervical cancer, while in the control group, 110 indicated they wanted the screening test. Construct a 90% confidence interval forP treatment - P control

4. A dermatologist in the US believes that cancers of the head and neck will occur most often of the left side in adults. In a review of 600 cases, 320 occurred on the left side. If the dermatologist's belief was tested to a 95% confidence, what would the p-value be?

5. In a sample of 51 adolescents who served as the subjects in an immunologic study, one variable of interest was the diameter of skin test reaction to an antigen. The sample mean and standard deviation were 28 and 15mm erythema, respectively. In a test to determine if the population mean is less than 32, what is the test statistic?