Q1. [Total 15 points] An IDS 270 student interviewed 200 vaccinated and 200 unvaccinated people in Chicago area to investigate whether they experienced a breakthrough Covid19 infection. Out of those who were vaccinated, 25 experienced a breakthrough infection. While out of those who were unvaccinated, 45 experienced a breakthrough infection. Execute a hypothesis test to determine whether there is a difference in the proportion of experiencing a breakthrough Covid-19 infection for vaccinated vs. unvaccinated people at alpha = 0.05. DO NOT USE CHI-SQUARE to solve this problem.

To solve the problem, follow the steps below:

a. n1 =

n2 =

X1 =

X2 =

b. State your hypotheses below:

Ho:

Ha:

Final Exam - Niket Prafulkumar Senjalia Page 2 of 6

c. Compute p-hat1

below: p-hat1 =

d. Compute p-hat2 below:

p-hat2 =

e. Compute p-hat below: p-hat =

f. Compute pooled standard error SEDp below: SEDp =

g. Compute z below: z =

h. Compute p-value below (hint: use Table A): p-value =

i. Do you reject Ho for Ha? Why?

j. State your conclusion in plain English:

Q2. The same student interviewed 200 vaccinated and 200 unvaccinated people in Chicago area to investigate whether they experienced a breakthrough Covid-19 infection. Out of those who were vaccinated, 25 experienced a breakthrough infection. While out of those who were unvaccinated, 45 experienced a breakthrough infection. Execute a hypothesis test to determine whether there is a relationship between the people's vaccination status (vaccinated or unvaccinated) and experiencing a breakthrough Covid-19 infection, at alpha = 0.05 USING CHI-SQUARE. To solve the problem, follow the steps below:

a. State your hypotheses below: Ho: Ha:

b. Fill in the relevant eight values in the following table (show your calculations):

Actual Vaccinated Unvaccinated Total Row % Experiencing the breakthrough infection (i) .......... (ii) .......... (iii) .......... (iv) .......... Not experiencing the breakthrough infection (v) .......... (vi) .......... (vii) .......... (viii) ..........

c. Fill in the relevant four values in the following table (show your calculations): Expected Vaccinated Unvaccinated Experiencing the breakthrough infection (i) .......... (ii) .......... Not experiencing the breakthrough infection (iii) .......... (iv) ..........

d. Fill in the relevant six values in the following table (show your calculations): Chi-squared Vaccinated Unvaccinated Experiencing the breakthrough infection (i) .......... (ii) .......... Not experiencing the breakthrough infection (iii) .......... (iv) .......... Total (v) ............ (vi) ..........

e. What is the Grand Total from the Chi-squared table in part d above? Grand Total =

f. Compute the df: df =

g. Compute the p-value below (Hint: use Table F): p-value =

h. Do you reject Ho for Ha? Why?

i. State your conclusion in plain English:

Q3. In each of questions 1 and 2, the student made a decision to reject Ho vs. not reject Ho. Was the outcome of these two decisions a coincidence, or not? Why or why not? Note: A coincidence is when two things happen but are not related. Circle one: Coincidence Not a coincidence -------------------------------------------------------------------------------------------------------------------------------- Why or why not?

Q4. The student also investigated the impact of Covid-19 pandemic on UIC students' academic performance by comparing their GPAs in the semester before the pandemic started and the one right after that. The test result showed that the average difference in GPA was 1.5, and the p-value for the test was 0.02. Assess the statistical and practical significance of the test result if alpha = 0.01.

a. Is it statistically significant? Circle one: Yes No -------------------------------------------------------------------------------------------------------------------------------- Why?

b. Is it practically significant? Circle one: Yes No -------------------------------------------------------------------------------------------------------------------------------- Why?

Q5. The student also executed a regression to predict the average GPAs (the dependent variable, or Y) using the number of absences (the independent variable, or X). The students expected that as the number of absences increases the GPA decreases.

a. [2 points] State Ho and Ha with regards to 1: Ho: Ha:

b. [2 points] The standard deviation of Y is 16. The square root of the sum of the squared residuals divided by n-2 equals 10 (note: the formula on slide 21 of Chapter 10). Does this suggest that the regression fits the data well? (No explanation required.) Circle one: Yes No -------------------------------------------------------------------------------------------------------------------

Q6. The student executes a hypothesis test with an alpha = 1% and rejects Ho for Ha.

a. What is the probability that the statistical conclusion is wrong?

b. If the student executed the same hypothesis test (with the above alpha) on different random samples of data 1,200 times, approximately how many times would it make the mistake of rejecting Ho when Ho is actually true in the population? Show your calculation below:

Q7. A population distribution has a symmetric shape.

a. What would be the shape of the sampling distribution?

b. The size of the samples used to build the three sampling distributions are 32, 47, and 57. Which one of these sample sizes has the tightest sampling distribution?

Q8. Match the notations or terms on the left with the correct definitions listed in the table.

a. Statistically significant

b. r 2 or r-squared

c. 0

d. Beta

e. Sample space

i. Mean of population ii. Mean of sample iii. Standard deviation of population iv. Standard deviation of a sample v. A variable that measures an outcome of a study. vi. A variable that explains changes in the dependent variable. vii. The correlation coefficient viii. The y-intercept of the least-squares regression line ix. The slope of the least-squares regression line x. The coefficient of determination xi. An observed effect so large that it would rarely occur by chance xii. A set of sample averages from same population xiii. A set of all possible outcomes xiv. The hypothesis we wish to reject xv. The hypothesis we wish to conclude xvi. The significance level xvii. The probability of Type II error