Question

Students at multiple grade schools were asked what their personal goal (get good grades, be popular, be good at sports) was and how important having money were to them (1 very important and 4 least important). The data is in the table below ("Popular kids datafile," 2013). Do the data provide enough evidence to show that goal attainment and importance of money are associated? Test at the 5% level.

Goal	Money Importance Rating				Row Total
	1	2	3	4
Grades	14	34	71	128	247
Popular	14	29	35	63	141
Sports	6	12	26	46	90
Column Total	34	75	132	237	478

Use the framework below to guide your work.

Hypotheses: :     

Ho: no relationship between goal attainment and importance of money

Ha: relationship between goal attainment and importance of money   

Blank #1: Test statistic = _________ (round to two decimal places)

Blank #2:  p-value = __________ (round to four decimal places)

Blank #3: Test decision: We decide to ___________ Ho (reject or do not reject)

Blank #4: Conclusion back into the words of problem: The evidence __________(favors or does not favor) that there is a relationship between goal attainment and importance of money.

Answer 1

Hypothesis :

H0 : There is no relationship between goal attainment and importance of money

H1: There is relationship between goal attainment and importance of money

We have to perform Chi-square independence Test.

Test statistic :

Where , O is observed frequency

E is expected frequency.

Where ,

Ri is total sum of ith row.

Cj is total sum of jth column.

Calculation :

The row(Ri) and column(Cj) total have been calculated and they are shown below :

The table below shows the calculations to obtain the table with expected values :

Based on the observed and expected values, the squared distances can be computed according to the following formula: (E−O)2/E

So test statistic is ,

0.725+1.572+0.025+0.583+2.137+0.319+0.114+0.398+0.053+0.25+0.683+0.042

6.90

P-value :

Using Excel function ,    =CHIDIST( ,df )

Test statistic = = 6.90

df = ( r - 1 )(c - 1 ) = ( 3 - 1 )( 4-1 ) = 6

( r is number of rows, c is number of columns )

P-value = CHIDIST( 6.90 , 6 ) = 0.330194

p-value = 0.3302

Decision about null hypothesis :

Rule : Reject null hypothesis if p-value less than significance level

Given , significance level = 5% = 0.05

It is observed that p-value greater than = 0.05

So, Do not reject null hypothesis.

Conclusion :

The evidence does not favor that there is a relationship between goal attainment and importance of money.