Question

question 3
1 pts
two competing hypotheses are put forward, as shown below, and a test statistic of 1.3 is
computed. based on this information, which one of the following conclusions is most
appropriate?
$h_o:p = 0.58$
$h_a:p > 0.58$
because $z = 1.3$, this tells us the $p$-value is just above the significance level.
at $\alpha = 0.10$, the evidence against the null hypothesis is barely sufficient to reject it.
at $\alpha = 0.05$, the evidence is strong enough to reject the null hypothesis.
since 0.01 falls below 1.3, we would reject the null hypothesis at $\alpha = 0.01$.
because this is considered a one - sided test, the test statistic should be divided in half before finding the $p$-value.

Explanation:

Step1: Find the P - value for \(z = 1.3\) in a one - sided test

For a one - sided (right - tailed) test with \(z=1.3\), we use the standard normal distribution table. The \(P\) - value is \(P(Z>1.3)\).
Since \(P(Z\leq1.3)=0.9032\) (from the standard normal table), then \(P(Z > 1.3)=1 - 0.9032=0.0968\).

Step2: Compare the \(P\) - value with different significance levels (\(\alpha\))

• For \(\alpha = 0.10\): Since \(P - value=0.0968<0.10\), we reject the null hypothesis \(H_0\).
• For \(\alpha = 0.05\): Since \(P - value = 0.0968>0.05\), we fail to reject the null hypothesis \(H_0\).
• For \(\alpha=0.01\): Since \(P - value=0.0968>0.01\), we fail to reject the null hypothesis \(H_0\).

The statement “At \(\alpha = 0.10\), the evidence against the null hypothesis is barely sufficient to reject it” is correct because \(P - value\approx0.097\) is just less than \(\alpha = 0.10\).

Answer:

At \(\alpha = 0.10\), the evidence against the null hypothesis is barely sufficient to reject it.