A study is conducted to determine if gender (0=female; 1= male) is associated with a diagnosis of Type 2 Diabetes Mellitus (t2dm: 0= absent; 1=present) on a group of patients, controlling for age. Results table are shown as below: Analysis of Maximum Likelihood Estimates   Estimate     Standard Error    Test statistic p-value Exp(B) Intercept -12.77      1.9759       41.8176        <.0001 ---------------- Gender 0.41 0.124    10.9799        0.0009 1.5 Age 0.0948      0.0305        9.6883        0.0019 1.09 What type of model is this, and why is this type of analysis appropriate in this case? Also, describe the finding: is gender associated with diagnosis of t2dm, why or why not (provide the test statistic and p-value)? Interpret the coefficient for gender and age.

A research team conducted a study of VARIABILITY in students' test performance. Researchers assume that individual records are normally distributed with unknown mean and variance. They collected a sample of n = 25 test scores with summaries shown below. Sample Mean = X = 75.2 and Sample SD = S = 15 1. At the significance level, a = 0.01, do researchers have sufficient evidence that the POPULATION VARIANCE would be ABOVE 120? • Show critical value • Evaluate Test Statistic • Formulate Rejection Rule • State your decision 2. At the significance level, a = 0.01, do researchers have sufficient evidence that the POPULATION VARIANCE would be BELOW 540? • Show critical value • Evaluate Test Statistic • Formulate Rejection Rule • State your decision Solution

Working at Home Workers with a formal arrangement with their employer to be paid for time worked at home, worked an average of 19 hours per week. A random sample of 14  mortgage brokers indicated that they worked a mean of 23.1  hours per week with a standard deviation of 6.5 hours. At α=0.05, is there sufficient evidence to conclude a difference? Construct a 95%  confidence interval for the true mean number of paid working hours at home. Compare the results of your confidence interval to the conclusion of your hypothesis test and discuss the implications. (a) State the hypothesis and identify the claim with the correct hypothesis. H0  H1  This hypothesis test is a one tailed/two-tailed test. (b)Find the critical value(s). Round the answer to 3  decimal places, if necessary. If there is more than one critical value, separate them with commas. Critical values:  (c)Compute the test value. Round the answer to at least 3  decimal places, if necessary. t= (d)Make the decision. Reject/do not…

It is estimated that in the general population about 9 out of every 1000 or 0.009 children are diagnosed with autism. on study included 92 six month old babies who had a sibling with autism. twenty-eight of these babies were later diagnosed with autism. we will systematically construct a 99% confidence interval for the proportion of siblings of autistic children likely to have autism.  What is the population being studied? What population parameter are we seeking to estimate? Describe this population parameter in words.