Week 10. Practice Problems
Math 2228—Elementary Stats
1.
Conduct a hypothesis test for the following scenario.
A study on heart transplants was conducted to determine whether an experimental heart transplant
program increased lifespan. Each patient entering the program was officially designated a heart transplant
candidate, meaning that they were gravely ill and might benefit from a new heart. Patients were randomly
assigned into treatment and control groups.
Patients in the treatment group received a transplant and
those in the control group did not. The table below displays how many patients survived an died in each
group
control
treatment
alive
12
24
dead
30
45
Is there a statistically significant improvement in the survival rate for those who received the treatment?
2.
Conduct a hypothesis test to answer the following research question.
The House of Representatives in 2019 is the most diverse in its history. But does it actually represent
the demographics of the US? The counts of House members by race are White (326), Black (52), Hispanic
(12), Asian (12) and American Indian (4). The proportion of US population for each race as of 2017 is
White (61.5%), Black (12.3%), Hispanic (17.6%), Asian (5.3%) and American Indian (0.9%).
Note, by
White, Black, Asian, and American Indian, we mean they are also non-Hispanic.
3.
Answer the following true/false questions and justify your answers:
(a) The chi-square distribution has two parameters: the mean and the standard deviation.
(b) As the degrees of freedom for the chi-square distribution increases, so does the mean.
(c) The p-value for a chi-square test-statistic inlcudes the area of two tails.
4.
The student body of the University of Fakestate has a total of 1430 undergraduates of which 1020 are
white, 180 are black, and 27 are American Indian. Is this representative of the population as recorded in
the 2000 census?
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