Question

question 4
1 pts
a publication states that 80% of college students own a laptop, but a researcher suspects this value is not high enough. when a random sample of 250 students is surveyed, 84% of the sample reports owning a laptop. based on this information, which one of the following statements is correct?
there is evidence against the null hypothesis since 0.84 is larger than 0.80.
if the researcher computes a negative value of z, this means an error was made when calculating the test statistic.
as long as the p - value is large, the researcher should conclude that there is evidence against the null hypothesis.
the hypothesis test will determine whether it is true that p = 0.84.
none of the above statements are correct.

Explanation:

• For the first option: Just because the sample proportion ($\hat{p}=0.84$) is larger than the hypothesized proportion ($p_0 = 0.80$) does not necessarily mean there is evidence against the null hypothesis. We need to perform a hypothesis - test (calculate the test - statistic and p - value) to make that determination.
• For the second option: The formula for the z - test statistic in a one - sample proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$. If $\hat{p}
• For the third option: A large p - value means we fail to reject the null hypothesis. We reject the null hypothesis when the p - value is small (less than the significance level $\alpha$).
• For the fourth option: The hypothesis test is to test the claim about the population proportion $p$ (in this case, the claim was originally about $p = 0.80$), not to test if $p = 0.84$ (0.84 is the sample proportion).

Answer:

None of the above statements are correct.