Question

Q3: Practice building Confidence Intervals For each scenario, take the sample data and build up the specified confidence interval for the specified population parameter. a. Scenario: You want to know the average number of calories you consume per day. Over the next 5 months you randomly select 25 days and carefully record your consumption on those days (assume that you don't change your eating habits) Build an 80% confidence interval for your average daily consumption of calories if the following represents the sample of 25 days: caloriesc (2543,2043,2654,1980,3400,256 0,2432,2034,2093,1983, 3004,2304,2739,2202,1823,250 4,2211,2340,2653,2342, 4030,2440,3034,2030,1990) b. Scenario: you are a political pollster getting the approval rating for Seattle's mayor. You poll n random people and find a 97% confidence interval of (0.4502, 0.4898). Find the number of people polled. Hint: first find fp and the z score for 97%, and then find n so that z-ơ, builds the confidence interval. p c. Scenario: students in the morning class vs. the afternoon class had the following scores on Exam 1 (percentage scores): morning_scoresc(74.04, 73.56, 66.83, 6 0.1, 30.29, 103.85, 30.77, 65.87, 48.56, 81.73, 77.4, 73.56, 38.46, 37.5, 23.56, 6 6.35, 70.19, 95.67, 85.1) afternoon, scores = c(69.07, 81.78, 47.46, 10 1.69,90.68,89.41,60.59,95.34,84.75,74.15, 78.39,83.9,54.24,91.1,53.39,86.44,83.05,6 4.41,80.08,81.36,88.56,79.66,66.95,71.19, 70.34,64.83,81.36,85.59,75,58.05,44.49,47 03,76.27) Suppose that Jen wants to determine if the exams are fair, and to do so she assumes that the students in each class are a random sample of all students who might take the exam, and she tries to determine if the two exams would have different averages in the full population. Build a 95% confidence interval for Ham Hpm using these (albeit not random) samples. Does it contain 0? Can you conclude anything about the fairness of the exams based on this? d. Suppose that, based on a sample of 81 different measurement locations, (47.8°F, 51.2 F) is a 90% confidence interval for the average surface temperature of Lake Washington when measured on April 10th. Reply True/False to each: Approximately 90% of the 81 measurement locations produced a temperature between 47.8 and 51.2 degrees F. It would be rare to take a sample that produced a confidence interval NOT containing the population mean, and so this confidence interval is likely to contain the population mean. If we were to build the 99% confidence interval, it would be narrower than (47.8,51.2) The standard deviation of individual iv. measurements in the sample was approximately 9.3°F

Answer 1

a)

Con fidence level 80 25 2454.72 503.6 1.3178 132.7288 2322 2587 Confidence interval is (2322, 2587)

b)

0.4502 0.4898

2.17

Now,

p(1 - p)

0.47(1-0.47) 0.4898-0.47 + 2.17

n 2992

Sann: 22.195 Spm- 14.681 anom2 324.1 npm idne Tutea(-1123-10-43 -11-23 +10.너3 (-21, 65,-0-5 ) honxe wre cam comelude that the

d)

i) False

ii) True

iii) False

iv) True