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 ≈ 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 α=0.01 significance level, they should conclude that the proportion has changed from 10%.b) At the α=0.01 significance level, they should conclude that the proportion is still 10%.c) At the α=0.05 significance level, they should conclude that the proportion has changed from 10%.d) At the α=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?

Question

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  ≈  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   α=0.01 significance level, they should conclude that the proportion has changed from 10%.b) At the   α=0.01 significance level, they should conclude that the proportion is still 10%.c) At the   α=0.05 significance level, they should conclude that the proportion has changed from 10%.d) At the   α=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?

snowman8842 · Accepted Answer

Two issues:(c) has 0.05 while (b) has 0.01Your choices are conventionally &quot;reject the null hypothesis&quot; or &quot;do not reject the null hypothesis&quot;, but not &quot;accept the null hypothesis&quot; which is close to the wording of (b) and (d)

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