Final Exam (1)

1. The Behavioral Risk Factor Surveillance System (BRFSS) is an annual telephone survey designed to identify risk factors in the adult population and report emerging health trends. The following table summarizes two variables for the respondents: health status and health coverage, which describes whether each respondent had health insurance.

(a) (2 points)  Find P (Good and No Coverage).  Write the both the fraction and decimal answer.

(b) (2 points) Find P(Good/No Coverage). Write the both the fraction and decimal answer

(c) (4 points) Is having no health coverage (health insurance) and having ‘Good’ Health independent?  Explain. You must include at least two probabilities in your reasoning.

2. According to the Insurance Journal, in 2018, 15.2% of Californian drivers do not have insurance. Due to COVID-19 you believe the number of people who are now driving without insurance has increased since more people would stop paying for insurance due to tough economic times. You take a random sample of 1030 drivers.

(a) (4 points) If the you decides to test this hypothesis at the α = 0.05 level of significance, determine the probability of making a Type II error if the true population proportion is 0.17. What is the power of the test? Sketch the relevant distribution(s) and region(s).

3. For the following scenario, sketch and find the critical value for α = 0.04.  Hint: Find the correct hypothesis first.

(a) (3 points) The average amount a specific student spends on eating out is $430 per month. After paying their cost, they feel that the amount they’ve spent recently is significantly higher than this

(b) (3 points) A soda filling machine at McDonald’s is supposed to dispense ice and 14 oz. of liquid into a medium sized cup. The machine will invariable experience fluctuation in this number (sometimes above and sometimes below). The machine is supposed to have a variability below 0.05 oz. A quality control engineer takes a sample to determine if the machine is broken (dispensing drinks with a higher variability in ounces).

(c) (3 points) Last-year it was found that 83% of GCC students support support the return of in-person classes. However, since we are now used to having remote classes we feel the support the return to in-person classes has decreased since then.

4. Two instructors wonder whether their students are doing well when compared to other classes. To investigate, one instructor randomly select 10 students in their class (call this ’Class 1’) and the other instructor selects 10 students(call this ’Class 2’).

(a) (2 points) Find two different measures of central tendency for each data set

(b) (2 points) Find two different measures of spread for each data set.

(c) (2 points) Use the above information to determine which class has scores which are more consistent to one another.  How do you know?

(d) (4 points) A student scores a 90 on a similar exam. In which class is this score a better score (relative to everyone else)? Hint: Use z-scores

5. (THIS IS THE SAME SCENARIO AND DATA AS PREVIOUS PROBLEM)
Two instructors wonder whether their students are doing well when compared to other classes. To investigate, one instructor randomly select 10 students in their class (call this ’Class 1’) and the other instructor selects 10 students(call this ’Class 2’).

(a) (2 points) Create a stem-and-leaf plot of Class 2 Data

(b) (2 points) Find a boxplot of each data set, sketch them on the same grid.

(c) (2 points) Find the five-number summaries for each data set.

(d) (4 points) A student scores a 115 on a similar exam. Is this grade unusual in either class? Explain.
Hint: Find the upper fence of each class.

6. (THIS IS THE SAME SCENARIO AND DATA AS PREVIOUS PROBLEM)
Two instructors wonder whether their students are doing well when compared to other classes. To investigate, one instructor randomly select 10 students in their class (call this ’Class 1’) and the other instructor selects 10 students(call this ’Class 2’)

(a) (2 points) The two samples are clearly ’Class 1’ and ’Class 2.’ Are the sample dependent samples or independent samples? Explain.

(b) (2 points) Write the hypothesis to test whether the mean grade on this exam is the same for both classes

(c) (4 points) Check the conditions for this hypothesis test

(d) (1 point) Find the test statistics for this test (no need to draw the distribution and critical value).

(e) (3 points) What is your conclusion? Answer the original questions.

7. Most people think that if a person wants to graduate from college then they will. However, there is some recent evidence to suggest that a student’s success in college depends on many factors. One factor influencing completion of a college education may be employment status. A researcher sampled students who started their college career in the Fall of 2017 to determine their Academic Status (whether they graduated or not).

Use a 0.01 significance level to determine if there is evidence to claim the proportion of students who graduated is the same across all employment types.

(a) (2 points) What are the hypotheses of this test?

(b) (3 points) Check the conditions are met to complete this hypothesis test?

(c) (4 points) Sketch the distribution curve, find the critical value(s) and your test statistics.

(d) (3 points) What is your conclusion. Answer the original question.

8. Scores for a previous statistics class on the final exam are tabulated below (each column represents the same student). Treat this as a random sample of student scores. Use the data (link in Canvas) below to answer the following:

(a) (3 points) Sketch a scatter diagram and discuss the relationship between the variables when treating the MyLab Score as the explanatory variable.

(b) (2 points) Use the correlation coefficient to determine whether there is a significant relation between the two scores.

(c) (2 points) Find the equation of the lease-square regression line treating the MyLab Score as the explanatory variable.

(d) (2 points) Interpret the slope and y-intercept of the equation.

(e) (3 points) Plot the residuals against MyLab Score. Provide the sketch below. Based on the residual plot only, do you think that a linear model is appropriate for describing the relation between the Free-Response Score and MyLab Score? Explain why (needs at least one full sentence)?