135k views
22 votes
A 2003 New York Times CBS news poll sampled 523 adults who were planning a vacation during the next 6 months and found that 141 were expecting to travel by airplane. A similar survey question in May 1993 New York Times CBS news poll found that of 477 adults who were planning to take a vacation in the next 6 months, 81 were planning to travel by airplane. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over 10 years.

1 Answer

6 votes

Answer:

The solution can be defined as follows:

Explanation:


H_0 : p_1 = p_2\\\\H_a : p_1 \\eq p_2\\

Testing the statistics values:


p_1 = (141)/(523) = 0.2696 \\\\ n_1 = 523\\\\p_2 = (81)/(477) = 0.1698\\\\ n_2 = 477


p = ((p_1 * n_1 + p_2 * n_2))/((n_1 + n_2))


= ((0.2696 * 523 + 0.1698 * 477))/(( 523 + 477))\\\\= ((141.0008 + 80.9946))/((1000))\\\\= ((221.99))/((1000))\\\\= ((222.0))/((1000))\\\\= 0.2220


SE = \sqrt{ p * ( 1 - p ) * [ ((1)/(n_1)) + ((1)/(n_2)) ] }


= \sqrt{( 0.222 * (1-0.222) *(((1)/(523)) + ((1)/(477))))}\\\\= 0.0263


z = ((p_1 - p_2))/(SE)


= (( 0.2696 - 0.1698))/(0.0263)\\\\= 3.7947

p = 0.0001

It reject all the null hypothesis values

User Meewog
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories