Question

According to a study conducted by an​ organization, the proportion of Americans who were afraid to fly in 2006 was 0.10. A random sample of 1 comma 400 Americans results in 154 indicating that they are afraid to fly. Explain why this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.

Answer 1

Answer: No, this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.

Explanation:

Since we have given that

n = 1400

x = 154

So,
`\hat{p}=(154)/(1400)=0.11`

and p = 0.10

So, hypothesis would be

`H_0:\hat{p}=p\\\\H_a:\hat{p}>p`

So, the test statistic value would be

`z=\frac{\hat{p}-p}{\sqrt{(p(1-p))/(n)}}\\\\z=\frac{0.11-0.10}{\sqrt{(0.1* 0.9)/(1400)}}\\\\z=(0.01)/(0.008)\\\\z=1.25`

At 5% level of significance,

critical value would be 1.96.

Since 1.96>1.25.

so, we will accept the null hypothesis.

Hence, no, this is not necessarily evidence that the proportion of Americans who are afraid to fly has increased.