Final answer:
In R, you can calculate a confidence interval for a population proportion using the prop.test function, where `x` is the number of dogs that compete, `n` is the total number of dogs, and conf.level is set to the desired confidence level.
Step-by-step explanation:
To calculate a confidence interval for the population proportion of dogs that compete in professional events, you can use the following R code snippet:
prop.test(x, n, conf.level = 0.95)
where x is the number of successes (dogs that compete), and n is the total number of trials (total number of dogs at the Dundee Dog Training School). The conf.level parameter represents the confidence level, which you can adjust to the desired confidence (for instance, 0.90 for a 90% confidence interval).
Here is an example with hypothetical data:
number_of_competing_dogs <- 35
total_dogs <- 50
prop.test(number_of_competing_dogs, total_dogs, conf.level = 0.95)
This R command will output the confidence interval along with other relevant test information. You can interpret the 95 percent confidence interval as the range within which we are 95% confident the true population proportion of competing dogs lies.