Question

question 8
1 pts
it is claimed that the proportion of high school athletes who go on to play sports in college is 0.08. believing the true proportion is not 0.08, a researcher surveys a random sample of former high school athletes and uses the resulting sample data to conduct a hypothesis test. when this test is conduct, it is reported that z = 1.9. from this information, what should we conclude?
because z = 1.9, we can conclude the sample size was at least 1,000.
the sample proportion must have been smaller than 0.08.
since \\( \hat { p } \\) is less than two standard deviations from p, the null hypothesis will be rejected only if \\( \alpha \\) is equal to or greater than 0.05.
the test statistic provides evidence that the true proportion exceeds 0.08, and this is the theory put forward by the alternative hypothesis.
the null hypothesis should not be rejected if \\( \alpha = 0.05 \\).

Explanation:

Step1: Analyze the z - value and significance level

For a two - tailed test, the critical z - values for \(\alpha = 0.05\) are \(z=\pm1.96\). The given \(z = 1.9\).

Step2: Compare the test statistic with the critical value

Since \(|z|=|1.9| = 1.9<1.96\) (the critical value for \(\alpha = 0.05\) in a two - tailed test).

Answer:

The null hypothesis should not be rejected if \(\alpha=0.05\).