Question

Chi-Square test

Question 1   Data have been collected over a period of several months on the means of transportation used by most persons commuting to work into the city office of a large business firm. The results have been listed below:

Means of Transportation	Bus	Train	Car	Other
Number of all commuters	25	15	50	10

Conduct a hypothesis test to determine if there is a significant difference among method of getting to work for this sample. Use a = 0.05.

Question 2 Influenza A is a virus which causes illness in humans and many other animal species. Once the virusfinds a host, it becomes a major concern and is fatal in some cases. A microbiologist wants to know if a person’s ageaffects the severity of conditions for people who contract Influenza A. Consider the table below and answer thequestions that follow.

	Outcome
	Mild conditions	Severe conditions
Child	114	167
Adult	124	112

a)  State the null and alternative hypotheses for this scenario.

1. Using the table above; calculate the expected values (two decimal places) for each outcome (write your answers in the table).

c)  Calculate the chi-square test statistic and degrees of freedom for this scenario.

d)  State your conclusion for this scenario (use a significance level of 0.01).

Answer 1

using minitab >stat>Tables

we have

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Number of all Commuters

Using category names in means of transportation

Test Contribution
Category Observed Proportion Expected to Chi-Sq
Bus 25 0.25 25 0
train 15 0.25 25 4
car 50 0.25 25 25
other 10 0.25 25 9

N DF Chi-Sq P-Value
100 3 38 0.000
Ans 10 ) H0: there is a significant no difference among method of getting to work for this sample

Ha:there is a significant difference among method of getting to work for this sample

since p value is less than 0.05 so we conclude that there is a significant difference among method of getting to work for this sample.

Ans 11) using minitab>stat>tables >chi square 'we have

Chi-Square Test for Association: data, outcome

Rows: data Columns: outcome

mild serve
conditions conditions All

child 114 167 281
129.4 151.6

adult 124 112 236
108.6 127.4

All 238 279 517

Cell Contents: Count
Expected count

Pearson Chi-Square = 7.402, DF = 1, P-Value = 0.007

a) the null and alternative hypotheses for this scenario. is

Ho :a person’s age do not affects the severity of conditions for people who contract Influenza A.

Ha:a person’s age affects the severity of conditions for people who contract Influenza A.

b) the expected values for each outcome is

child 114 167 281
expected   129.4 151.6

adult 124 112 236
expected 108.6 127.4

Ans )the chi-square test statistic = 7.402

and degrees of freedom = 1

d) p value =0.007 whic is less than 0.01 so we reject Ho and conclude that a person’s age affects the severity of conditions for people who contract Influenza A.