Question

In 1997, 46% of Americans said they did not trust the media when it comes to reporting the news and fairly. In 2007 poll of 1010 adults nationwide, 525 stated they did not trust media. At the α=0.05 level of significance, is there evidence to support the claim that the percentage of Americans that do not trust the media to report fully and accurately has increased since 1997

Answer 1

We can conclude that the percentage of Americans that do not trust the media to report fully and accurately has increased since 1997 (P-value=0.00014).

Explanation:

We have to perform an hypothesis test on a proportion.

The null and alternative hypothesis are:

`H_0: \pi=0.46\\\\H_1: \pi>0.46`

The significance level is α=0.05.

The standard deviation is estimated as:

`\sigma=\sqrt{(\pi(1-\pi))/(N) } =\sqrt{(0.46(1-0.46))/(1010) }=0.0157`

The z value for this sample is

`z=(p-\pi-0.5/N)/(\sigma) =(525/1010-0.46-0.5/1010)/(0.0157) =(0.52-0.46-0.00)/(0.0157)=(0.06)/(0.0157) =3.822`

The P-value for z=3.822 is P=0.00014.

The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.

We can conclude that the percentage of Americans that do not trust the media to report fully and accurately has increased since 1997.