A clinical researcher wants to see whether a new medicine will help reduce blood sugar level. She randomly selects 20 persons and assigns them to the new medicine (length of the program is three months). For each person she records their blood sugar level as they start the medicine and after they complete the program. To test whether mean reduction in blood sugar level is significant, we would do:

State whether below statement is either a True or a False statement. If it is false explain why. Please note that you can say something is true if it’s always true. Suppose we are testing the effectiveness of two drugs A and B in timely pain relief. Drug A was tested on a random sample of 20 patients, and has mean relief time of 10.3 minutes with standard deviation of 2.2 minutes. Drug B was tested on another 20 patients, and has mean relief time 8.3 minutes and standard deviation of 2.8 minutes. Based on our “rule of thumb”, we cannot use the pooled estimate of the standard error.      

Please note that this question consists of six parts. You need to show all mathematical calculations to get the final answer. Just giving the answer without showing work may result in zero for the question.  A research group is interested in determining whether teenagers obtain their drivers licenses at approximately the same average age across the country. Data on the age at which teenagers obtained their drivers license are randomly collected from teenagers in each of five different regions of the country. Research group who conducts the study have decided to use One-way ANOVA to compare the mean age at which teenagers obtained their drivers license for the five regions tested. They need help from a statistician to interpret the results. Use provided partial output to answer the following questions. Write down the null and alternative hypotheses for testing whether or not the mean age at which teenagers obtained their drivers license are the same for the five regions tested. Use properly defined parameters when you set up null and alternative hypotheses. Compute the degrees of freedom missing in the ANOVA output (i.e. error degrees of freedom) Compute the sum of squares missing in the table (i.e.: Sum of square treatment)  Compute the F-value missing in the ANOVA output. At a 5% significant level is there sufficient evidence to claim that the true mean age at which teenagers obtained their drivers license is different for at least one of the regions. Explain your answer. The output for Tukey pairwise comparisons is given below. Based on the output Are the mean age at which teenagers obtained their drivers license for the regions of East and Norteast significantly different? Explain your answer. Which region seems to have the highest mean age at which teenagers obtained their drivers license?    

Here are copies of Z-table and T-table.  Z table.pdf T_table.pdf  

Please note that this question consists of five parts. Show all your work. Just giving the answer without showing work may result in zero for the question.  Data from a simple random sample of 121 Penn State seniors were collected. As a part of the study, they were asked below two questions: What is your current GPA? Are you planning on applying to graduate school? For the sampled 121 students, the average GPA is 3.6 and the standard deviation is 0.36. Find a 95% confidence interval for the average GPA of Penn State seniors.   A recent study claims that the average undergraduate GPA in U.S. universities is about 3.4. Based on your calculation in part 1, are Penn State seniors doing better in terms of their GPA? In the sample of 121 students, 18 said they plan on applying to graduate school. Find a 95% confidence interval for the proportion of Penn State seniors who plan on going to graduate school.  What conditions need to be satisfied in order for you to calculate the confidence interval in part 3? Are they satisfied? Rather than constructing a confidence interval, I decided to carryout the below hypothesis test.  Formulated hypothesis is:

For each of the following, select the correct answer from the dropdown menu.  If A and B are mutually exclusive events then P(A) = P(B) = 0.5 This is a statement.  If A and B are independent events, then

Please note that this question consists of three parts. Show all your work/explanation. Just giving the answer without adequate work/explanation may result in zero for the question.  Fifty six percent of the undergraduate students in a college lives off-campus, 68% have a car, and 49% live off-campus and have a car. We randomly select an undergraduate student. Are the events “living off-campus” and “have a car” mutually exclusive? Explain your answer.   What is the probability that the student neither lives off-campus nor have a car? What is the probability that he/she has a car, if he/she lives off-campus?

Please note that this question consists of six parts. You need to show all mathematical calculations to get the final answer. Just giving the answer without showing work may result in zero for the question. Are the means for the final exams same for all statistics class delivery types? Data on the scores on final exams from several randomly selected classes that used the different delivery types – Face-to-Face, Hybrid, Online are obtained. Purpose of the study was to determine whether the average scores on final exams would be the same for all three different delivery types.  Research group who conducts the study have decided to use One-way ANOVA to compare the mean scores on final exams. They need help from a statistician to interpret the results. Use provided partial output to answer the following questions. Write down the null and alternative hypotheses for testing whether or not the average scores on final exams would be same for all three different delivery types. Define the parameters and use those defined parameters when you set up null and alternative hypotheses. Compute the degrees of freedom missing in the ANOVA output (i.e. error degrees of freedom) Compute the sum of squares missing in the table (i.e.: Sum of square treatment)  Compute the F-value missing in the ANOVA output. At a 5% significant level is there sufficient evidence to claim that the true average scores on final exams are different for at least one of the delivery types. Explain your answer. The output for Tukey pairwise comparisons is given below. Based on the output Is the average final exam scores for Face-to-Face and Hybrid are significantly different? Explain your answer. Which class type seems to have the highest average final exam score?      

A certain university is divided into six colleges, with most students graduating from four of these colleges. The following bar chart gives the distribution of the percent graduating from the four most popular colleges in 2019. The percent of students graduating from either engineering or business is:      

A student organization wanted to see who lives on-campus and who lives off-campus. They selected 100 students at random from each class, freshmen through seniors. The sampling technique being used is: