Confidence level	90%	95%	99%
z*	1.64	1.96	2.58

1. A nutritionist would like to determine the proportion of OSU students who are vegetarians. He surveys a random sample of 585 OSU students and finds that 54 of these students are vegetarians. From this information, calculate the sample proportion below and round your answer to three decimal places.

2. Would we call the value you computed to answer Question 1 a parameter or a statistic? Please explain.

3. The nutritionist decides to construct a 99% confidence interval to estimate the population proportion of OSU students who are vegetarians. In your opinion, what might be a reason for choosing to construct a 99% confidence interval as opposed to a 90% or a 95% confidence interval?

4. Using the information provided in Question 1, construct a 99% confidence interval and show all work below. Be sure to clearly label your upper and lower bounds.

Lower bound:

Upper bound:

5. Based on the interval you constructed to answer Question 4, complete the following statement.

We are 99% confident that the interval from _________ to ________ includes ________________________________________________________________________________________________________________________________________________.

6. Using the same information presented in Question 1, construct a 90% confidence interval. Again, show all work below and make it clear what your lower and upper bounds are.

Lower bound:

Upper bound:

7. Compare the 99% and 90% confidence intervals that you constructed. What is different about these intervals?

8. In general, when we construct a confidence interval, we want to obtain as precise of an estimate as possible of the unknown population parameter. Look carefully at the following five combinations of sample size and confidence level that the nutritionist could have used to obtain his estimate. Which combination would lead to the most precise estimate?

a. n = 1500, confidence level = 99%

b. n = 1500, confidence level = 90%

c. n = 585, confidence level = 99%

d. n= 585, confidence level = 90%

e. n = 100, confidence level = 90%

9. Please explain the reason for the answer you chose for Question 8.

Part 2: Exercising your reasoning skills

The following questions might be more challenging. Many of them extend what we have discussed and do not exactly match examples presented in the textbook or in lecture. However, we still want you to wrestle through these questions and ask for clarification along the way. We hope that ultimately, working through these more challenging problems will strengthen your understanding of the big ideas behind confidence intervals.

10. What proportion smartphone users own an Android phone? A 95% confidence interval is constructed in order to estimate this unknown population proportion. The interval ends up being from 0.39 to 0.47. Based on this interval, we know the sample proportion must be __________________ and the margin of error must be _____________ .

11. A random sample of adults is surveyed about the one musical performer they think should be inducted into the Rock & Roll Hall of Fame in 2022. The proportion of the sample who say Pat Benatar is 0.33. Imagine that data from this sample is used to construct a confidence interval in order to estimate the proportion of all adults who think Pat Benatar should be inducted into the Rock & Roll Hall of Fame. Look carefully at the five confidence intervals presented below. Which one of these intervals could not possibly be a proper interval based on what you know about this sample?

a. 0.32 to 0.34

b. 0.25 to 0.41

c. 0.31 to 0.42

d. 0.30 to 0.36

e. 0.29 to 0.37

12. What proportion of undergraduate students are in favor of plans to increase the number of online course offerings? When a college administrator surveys a random sample of undergraduate students and constructs a 90% confidence interval, she reports the interval as being from 0.356 to 0.397. If the administrator had constructed a 95% confidence interval instead of a 90% confidence interval, the 95% confidence interval would have been

a. wider and would have a smaller chance of missing the true population proportion.

b. narrower and would have a smaller chance of missing the true population proportion.

c. wider and would have a larger chance of missing the true population proportion.

d. narrower and would have a larger chance of missing the true population proportion.

e. wider, but the chance of missing the true population proportion cannot be determined.

13. True or False? Doubling the population size will have no impact on the width of a confidence interval.

14. An administrator at Milpitas High School would like to estimate, with 95% confidence, the percentage of students who will enroll in summer courses. Based on a random sample of data that is gathered, a 95% confidence interval is constructed. The interval is 15% 3%. If there are 2400 students who attend Milpitas High School, and if the administrator is estimating, with 95% confidence, that 15% 3% of these students will enroll in summer courses, this means the possible number of students who might enroll in summer courses is from

a. 120 to 760 students.

b. 288 to 432 students.

c. 404 to 486 students.

d. 362 to 548 students.

e. 280 to 600 students

15. A 95% confidence interval is constructed in order to estimate the proportion of adults who own an iPhone. The resulting interval has a margin of error of 0.043. Which of the following would be the margin of error for a 90% confidence interval based on the same sample of data?

A. 0.022

B. 0.018

C. 0.054

D. 0.036

E. It is impossible to answer this question without more information.