Question

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.

Answer 1

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