# 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% versus H_a:p=!10% 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 aprox 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?

Kevin Charles 2022-10-11 Answered
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?
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## Answers (1)

snowman8842
Answered 2022-10-12 Author has 12 answers
Two issues:
(c) has 0.05 while (b) has 0.01
Your choices are conventionally "reject the null hypothesis" or "do not reject the null hypothesis", but not "accept the null hypothesis" which is close to the wording of (b) and (d)
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