Final answer:
To determine whether there is evidence that the true population proportion of children who have ADHD is different than 20%, we can perform a hypothesis test. The null and alternative hypotheses are set up, and the p-value is calculated using a binomial test and the normal approximation. Based on the calculated p-value and the significance level, a conclusion is made.
Step-by-step explanation:
To determine whether there is evidence that the true population proportion of children who have ADHD is different than 20%, we can perform a hypothesis test. First, let's state the null and alternative hypotheses:
Null hypothesis (H0): The true population proportion of children who have ADHD is 20%
Alternative hypothesis (Ha): The true population proportion of children who have ADHD is different than 20%
To conduct the hypothesis test, we calculate the p-value. If the p-value is less than the significance level (0.05 in this case), we reject the null hypothesis. If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis.
In this case, based on the study, the proportion of children with ADHD is 25%. To calculate the p-value, we can use a binomial test. If the number of successes (children with ADHD) is at least 10 in the sample, we can use a normal approximation. Using the normal approximation, we can calculate the standard error as the square root of (p*(1-p)/n), where p is the proportion of children with ADHD in the sample (0.25) and n is the sample size (200).
Then, we can calculate the z-score as (p - p0) / SE, where p0 is the hypothesized proportion (0.2 in this case).
Using the z-score, we can calculate the p-value using a standard normal distribution table or a calculator.
Based on the calculated p-value, we can make a conclusion. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence that the true population proportion of children who have ADHD is different than 20%. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a difference in the population proportion of children who have ADHD.