Question

It is believed that 5% of all people requesting travel brochures for transatlantic cruises actually take the cruise within 1 year of the request. An experienced travel agent believes this is wrong. Of 100 people requesting one of these brochures, only 3 have taken the cruise within 1 year. We want to test the travel agent's theory with a hypothesis test. Calculate the p-value for this test.

Answer 1

The p-value for this test is 0.3576 using the travel’s agent theory with a hypothesis test.

Step-by-step explanation:

To calculate p-value for this test, we need a test statistic which can be obtained if we know the sample proportion.

`\text { So, sample proportion, } \hat{p}=(x)/(n)`

`\text { Where } x=\text { the people who have taken cruise within } 1 \text { year }=3, \text { and } n=\text { sample size }=100`

`\text { Now, } \hat{p}=(3)/(100)=0.03`

`\text { Now test statistic, } z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}`

`Z=\frac{0.03-0.05}{\sqrt{(0.05(1-0.05))/(100)}}`

`z=-0.92`

`\text { Here, } \mathrm{p}=\text { hypothesis test }=0.05`

`\text { Therefore, p-value for this test }=2 * \text { NORMDIST(- } 0.92)`

`\text { p-value for this test }=2 P(z<-0.92)`

`\text { p-value for this test }=0.3576`

Hence, the p-value for this test is 0.3576 using the travel’s agent theory with a hypothesis test.