A poll from a previous year showed that 10% of smartphone owners relied on their data plan as their primary form of internet access. Researchers were curious if that had changed, so they tested ${H}_{0}:p=10\mathrm{\%}$ versus ${H}_{a}:p\ne 10\mathrm{\%}$ where p is the proportion of smartphone owners who rely on their data plan as their primary form of internet access. They surveyed a random sample of 500 smartphone owners and found that 13% of them relied on their data plan.

The test statistic for these results was $z\approx 2.236$, and the corresponding P-value was approximately 0.025.

Assuming the conditions for inference were met, which of these is an appropriate conclusion?

a) At the $\alpha $=0.01 significance level, they should conclude that the proportion has changed from 10%.

b) At the $\alpha $=0.01 significance level, they should conclude that the proportion is still 10%.

c) At the $\alpha $=0.05 significance level, they should conclude that the proportion has changed from 10%.

d) At the $\alpha $=0.05 significance level, they should conclude that the proportion is still 10%.

The correct answer is c but why could it not have been b? Why is it c?

The test statistic for these results was $z\approx 2.236$, and the corresponding P-value was approximately 0.025.

Assuming the conditions for inference were met, which of these is an appropriate conclusion?

a) At the $\alpha $=0.01 significance level, they should conclude that the proportion has changed from 10%.

b) At the $\alpha $=0.01 significance level, they should conclude that the proportion is still 10%.

c) At the $\alpha $=0.05 significance level, they should conclude that the proportion has changed from 10%.

d) At the $\alpha $=0.05 significance level, they should conclude that the proportion is still 10%.

The correct answer is c but why could it not have been b? Why is it c?