Question

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.

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

a)

H₀ : Injury is independent of floor type.

H₁ : Injury is not independent of floor type.

b)

Considering 1 as injured and 0 as not injured the 2X2 contingency table is as follows

	Injured	not injured	Marginal Row Totals
Standard Floor	7	9	16
Rubber Floor	3	5	8
Marginal Column Totals	10	14	24

Expected frequency E_ij =

	Injured	not injured	Marginal Row Totals
Standard Floor	7   (6.67)	9   (9.33)	16
Rubber Floor	3   (3.33)	5   (4.67)	8
Marginal Column Totals	10	14	24

test statistic

The chi-square statistic is 0.0857

c) The p-value is 0.769698

d) Sine p-values is more than level of significance we fail to reject null hypothesis and conclude that injury type is independent of floor type.

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

The assumption required for the validity of hypothesis test is " Expected counts should be atleast 5".