Final answer:
The level of a test for which H0 is rejected if x ≤ 16.00 is found through normal approximation to the binomial, with the critical z-score for alpha = 0.05 being -1.645. If the study's z-test value is less than -1.645, H0 is rejected, indicating the p-value is less than alpha, providing sufficient evidence against the null hypothesis.
Step-by-step explanation:
To determine the level of the test when it's decided to reject H0 (the null hypothesis) if x ≤ 16.00, one can use the normal approximation to the binomial. Given that the sample size (n) is 15 and the significance level (alpha) is 0.05, we look at the standard normal distribution to find the critical value.
The z-score corresponding to an alpha level of 0.05 is -1.645 when considering a left-tailed test. This z-score falls between -1.65 and -1.64 on the standard normal distribution table. If the calculated z-score based on the sample mean is less than -1.645, the null hypothesis is rejected.
For example, if a study's parameter p is given and expected to be around 0.8, the z-test can be calculated using the sample proportion. If the z-test value is less than -1.645, it confirms that alpha > p-value, leading us to reject the null hypothesis.
In conclusion, for the given decision rule with x ≤ 16.00, by comparing the alpha and the p-value for a sample, one can decide whether there is sufficient evidence to reject H0.