Question

A researcher in a large city was interested if the type of transportation people prefer to use (i.e., City Bus or Own Car) is correlated with their sleeping habits (i.e., typically going to bed Before Midnight or typically going to bed After Midnight). The data collected by an online survey from a sample of n=110 participants are presented  in the following frequency distribution table (note: the number in each cell represents a count of people in each category):

Sleeping Habits	City Bus	Own Car
In Bed BEFORE midnight	20	25
In bed AFTER midnight	50	15

Based on these results, can the researcher conclude that there is a significant

relationship between sleeping habits and preferred transportation type? Test at p < .05 level of significance.

Your answer should include:

         - hypotheses

         - computed Chi² (show all computational steps)

         - df and critical Chi² for p <.05

         - the decision about H₀ and the conclusion in APA reporting format

   - if the relationship is statistically significant, compute the phi-coefficient to

measure the strength of the relationship

Answer 1

null hypothesis :Ho: sleeping habits and preferred transportation type are not related

Alternate hypothesis:Ha: sleeping habits and preferred transportation type are related

Applying chi square test:

Expected	Ei=row total*column total/grand total	City Bus	Own Car	Total
	before	28.64	16.36	45
	after	41.36	23.64	65
	total	70	40	110
chi square    χ2	=(Oi-Ei)2/Ei	City Bus	Own Car	Total
	before	2.6046	4.5581	7.163
	after	1.8032	3.1556	4.959
	total	4.408	7.714	12.1215

computed Chi square X² =12.1215

degree of freedom(df) =(rows-1)*(columns-1)=

1

critical Chi square X² =3.841

as test statistic is is higher than critical value ; we reject null hypothesis and conclude that sleeping habits and preferred transportation type are related

phi-coefficient =sqrt(X² /n) =0.332