Question

question 2
facebook for college students. a study suggests that 60% of students spend more than 10 hours on facebook each week. you believe that this is wrong. with your friend’s help, you randomly sample 160 college students. you find that 70% spent 10 or more hours a week on facebook.
your friend writes the following set of hypotheses, making some mistakes:
$h_0: \hat{p} < 0.60$
$h_a: \hat{p} > 0.70$
what did your friend do wrong? describe their mistakes by picking from the choices below.

• the hypotheses should use the symbol p, not the symbol \hat{p}.
• the hypotheses should both use the proportion 0.60, not 0.70.
• the null hypothesis ($h_0$) should be $p \leq 0.60$.
• the null hypothesis ($h_0$) should be $p \

eq 0.60$.

• the alternative hypothesis ($h_a$) should be $p \

eq 0.60$.

• the null hypothesis ($h_0$) should be $p = 0.60$.

Explanation:

Hypotheses test population parameters (p, true proportion), not sample statistics ($\hat{p}$). The null hypothesis ($H_0$) should state the original claim (0.60) with equality, and the alternative ($H_A$) should contradict it. The friend used $\hat{p}$ instead of p, set $H_0$ to <0.60 (no equality) and $H_A$ to >0.70 (wrong value). Correct issues: use p, $H_0$ has =0.60, $H_A$ uses 0.60.

Answer:

The hypotheses should use the symbol 'p', not the symbol '$\hat{p}$'
The hypotheses should both use the proportion '0.60', not '0.70'
The null hypothesis ($H_0$) should be 'p = 0.60'