Question

Although Puerto Rico is a territory of the United States, there are many cultural differences between the states and the island. These differences include the way that the consumers handle problems with purchases. Two researchers surveyed owners of VCR's in the northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCR's whether they had complained.

Complained Northeast, USA Puerto Rico

No 94 33

Yes 330 64

what do we know about the p value for testing the null hypothesis that the probability of complaining is the same for the united states and puerto rico?

Answer 1

• Here we have to test the claim that complaining is independent on united states and puerto rico.
• Since here we are for dependence we will use chi square test statistics
• HYPOTHESIS TO BE TESTED.
• here let the null hypothesis be that complaining is independent on united states and puerto rico.
• Let the alternate hypothesis be that complaining is dependent on united states and puerto rico.
• TEST STATISTICS
• (O-E)^2/E~X^2
• The expected frequency is given

• ( row total *column total )/table total

• complaint	north east	usa puerto rico	Total
  no	103.35551	23.64491	127
  yes	320.6449	73.35509	394
  Total	424	97	521

• The test statistics is given by

• 

• complaint	north east	usa puerto rico
  no	0.846767	3.701331
  yes	0.272943	1.193068
  total			6.01410

• The degrees of freedom is given by

• The degrees of freedom associated with a table with r rows and c columns is:

• (rc-1)-(r-1)-(c-1)=(r-1)*(c-1)=1

• CONCLUSION

• The critical value at 5% significant level with 1 degrees of freedom is given by 3.841

• The test statistics obtained is greater than 5% critical value.

• Hence we do have enough evidence to reject the null hypothesis.

• Hence we conclude that complaining is dependent on united states and puerto rico.