Answer:
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).
Step-by-step explanation:
We have to perform an hypothesis test on a proportion.
The null and alternative hypothesis are:
[tex]H_0: \pi=0.46\\\\H_1: \pi>0.46[/tex]
The significance level is α=0.05.
The standard deviation is estimated as:
[tex]\sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.46(1-0.46)}{1010} }=0.0157[/tex]
The z value for this sample is
[tex]z=\frac{p-\pi-0.5/N}{\sigma} =\frac{525/1010-0.46-0.5/1010}{0.0157} =\frac{0.52-0.46-0.00}{0.0157}=\frac{0.06}{0.0157} =3.822[/tex]
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.
