Question

4. A researcher conducts an experiment in a residence for senior citizens to investigate the effect of floor type on the risk of fall-related injury. For 24 randomly selected individuals in the facility, she records the type of flooring (either standard flooring or a new, rubber flooring that absorbs the impact of falls) in their room and whether they sustained at least one fall-related injury in their room over the previous two years. She is interested in whether the rubber flooring is associated with a reduced risk of injury. Her data are available in the file fall.csv.

"Floor","Injury"

"Standard",0

"Standard",1

"Standard",0

"Standard",1

"Standard",1

"Standard",0

"Standard",0

"Standard",1

"Standard",0

"Standard",0

"Standard",1

"Standard",0

"Standard",1

"Standard",0

"Standard",0

"Standard",1

"Rubber",0

"Rubber",0

"Rubber",0

"Rubber",1

"Rubber",1

"Rubber",0

"Rubber",0

"Rubber",1

a. What are the null and alternative hypotheses?

b. What is the value of the test statistic?

c. What is the p-value?

d. State your conclusions in the language of the problem. Use a significance level of 10%.

e. Which assumption is required for the validity of your hypothesis test and why might it be reasonable in this context?

Answer 1

Answer a)

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: There is no association between flooring and injury

Ha​: The is association between flooring and injury

Answer b)

Answer c)

P-value corresponding to χ² = 0.0857 and df = (r-1)*(c-1) = (2-1*(2-1) = 1 is 0.7697

(Obtained using online p-value calculator. Screenshot attached)

Answer d)

Since p = 0.7697 > α = 0.10, we fail to reject null hypothesis. Thus, there is not enough evidence to support the claim that the rubber flooring is associated with a reduced risk of injury.

********Dear Student We can answer first 4 parts only********