PROBLEM 3 - Music Choices Situation: Groups of 30-year-olds were interviewed to

Question

PROBLEM 3 - Music Choices

Situation:

Groups of 30-year-olds were interviewed to determine whether the type of music most listened to by people in their age category is independent of the geographic location of their residence.

Action:

Use the chi-square test of independence, a = .01, and the following contingency table to determine whether music preference is independent of geographic location. Show the steps of hypothesis testing relevant to this problem and its type of test statistic and make a decision. Explain what that decision means.

Type of Music Preferred Rock R&B; Country Classical Geographic Northeast 140 134 41 154 27 18 South West 52 Region 13

Explanation / Answer

Sol:

Null hypothesis:

music preference is independent of geographic location

Alternative Hypothesis:

music preference is dependent of geographic location

alpha=0.01

Chi sq test of independence

Calculate Expected Frequencies

Expected Frequency=row tot*col tot/Grand total

E(140)=195*428/632=132.057

E(32)=195*100/632=30.854

E(5)=195*65/632=20.055

E(18)=195*39/632=12.033

E(134)=235*428/632=159.146

E(41)=235*100/632=37.184

E(52)=235*65/632=24.169

E(8)=235*39/632=14.502

E(154)=202*428/632=136.797

E(27)=202*100/632=31.962

E(8)=202*65/632=20.775

E(13)=202*39/632=12.465

Create chi sq table:

p vlaue<0.00001

Reject Null hypothesis.

Accept alternative Hypothesis.

There is no suffiicient statistical evidence at 1% level of signiifcance to conclude that music preference is independent of geographic location.

music preference is dependent of geographic location.

Degrees of freedom=(no of rows-1)(no of columns-1)

=(3-1)(4-1)

= 2*3

=6

ROCK B&B Country Classical Rowtoa NE 140 32 5 18 195 S 134 41 52 8 235 W 154 27 8 13 202 Col Tot 428 100 65 39 632

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