Question

Some travel agents claim that honeymoon hot spots vary according to age of the couple. Suppose that 280 East Coast residents who recently get married were inter- viewed as to where they spent their honeymoons. The information is given below. Conduct a hypothesis test for independence, using a = = 0.10. Location 20 29 30 - 39 40 - 49 50 and over Niagara Falls 15 25 20 Poconos 15 25 25 10 Europe 10 15 5 Virgin Islands 20 25 15 5 25 25

Answer 1

Expected Values 20 to 39 30 to 39 40 to 49 50 and over Total Niagara falls 60 x 85 280 = 18.214 100 x 85 280 = 30.357 80 x 85 280 = 24.286 40 x 85 280 = 12.143 85 Poconos 60 x 75 280 = 16.071 100 x 75 280 = 26.786 80 x 75 = 21.429 40 x 75 280 10.714 75 280 Europe 60 x 55 280 = 11.786 100 X 55 280 = 19.643 80 x 55 280 = 15.714 40x55 280 = 7.857 55 Virgin Islands 60 x 65 280 = 13.929 100 x 65 280 = 23.214 80 x 65 280 = 18.571 40 x 65 280 = 9.286 65 Total 60 100 80 40 280

Squared Distances 20 to 39 30 to 39 40 to 49 50 and over Niagara falls (15-18.2142 18.214 = 0.567 (25-30.357) 30.357 = 0.945 (25-24.286)2 24.286 = 0.021 (20-12.143) 12.143 = 5.084 Poconos (15-16.071)2 16.071 = 0.071 (25-26.786) 26.786 0.119 (25-21.4292 21.429 = 0.595 (10-10.714) 10.714 = 0.048 Europe (10-11.786) 11.786 = 0.271 (25-19.643) 19.643 = 1.461 (15-15.714) 15.714 = 0.032 (5-7.857) 7.857 = 1.039 Virgin Islands (20-13.9292 13.929 = 2.647 (25-23.214) 23.214 0.137 (15-18.571) 18.571 = 0.687 (5-9.286)2 9.286 = 1.978

Null and Alternative Hypotheses

Ho: The two variables are independent H,: The two variables are dependent

Rejection Region

The degree of freedom, df = (4 – 1) * (4 - 1) = 9

The Critical value is 14.684

Test Statistics

η χ’ –Σ (Ο) - Ε;;)? Eij i=1

= 15.703

The P value is 0.0734

Decision about the null hypothesis Since it is observed that x2 = 15.703 > xả = 14.684, it is then concluded that the null hypothesis is rejected.

Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.10 significance level.