Question

Life after college. We are interested in estimating the proportion of graduates at a mid-sired university who found a job within one year of completing their under craduate degree. Suppose we conduct a survey and find out that 348 of the 100 randomly sampled graduate found jobit. The graduating class under consideration included over 4500 students. (a) Describe the population parameter of interest. Whist is the value of the point estimate of this parameter (b) Check if the conditions for constructing a confidence interval based on these data are met (c) Calculate n 95% confidence interval for the proportion of graduates who found a job within one year of completing their undergraduate degree at this tiniversity, and interpret it in the context of the data (d) What does 95% confidence mean? (e) Now calculate a 99% confidence interval for the same parameter and interpret it in the context of the data. (f) Compare the width of the 95% and 99% confidence intervals. Which one in wider? Explain

Answer 1

see below

Step-by-step explanation:

(a) The population parameter of interest is the proportion of all graduates who found a job within one year of completing their degree. The point estimate of this parameter from the sample is approximately 0.348.

(b) The conditions for constructing a confidence interval are met: The sample is random, and it's less than 10% of the population size.

(c) A 95% confidence interval for the proportion of graduates who found a job is calculated, indicating a range within which the true proportion likely falls.

(d) A 95% confidence level means that in repeated sampling, about 95% of the confidence intervals constructed would contain the true population proportion.

(e) A 99% confidence interval is calculated, which is wider than the 95% interval, providing a higher level of confidence.

(f) The 99% confidence interval is wider than the 95% interval because it accommodates a higher level of confidence, which requires a broader range of possible values to contain the true proportion.