Stat 2 Lab #17: The Sample Percentage

University:
University of California, San Diego
Course:
CSE 100/101 | Data Structures and Algorithms
Academic year:

2023
Views:

333

Pages:

3
Author:

Sol Kwon

Stat 2 Lab #17: The Sample Percentage Learning objectives: • Construct box models for classifying and counting • Calculate the expected values and SEs for a sample percentage • Use the normal approximation to calculate the chances of sample percentages falling into an interval • Reason about the accuracy of sample percentages with different sample sizes. 1. 500 draws are made at random from the box containing 60,000 tickets labeled 0 and 20,000 tickets labeled 1. Draw a picture as I did at the beginning of Lecture 52 to illustrate doing this repeatedly and keeping track of the sample percentage of 1’s. Now answer TRUE or FALSE for each, and explain briefly: (a) The expected value for the percentage of 1’s among the draw is exactly 25%. (b) The expected value for the percentage of 1’s among the draws is around 25%, give or take 2% or so. (c) The percentage of 1’s among the draws will be around 25%, give or take 2% or so. (d) The percentage of 1’s among the draws will be exactly 25%. (e) The percentage of 1’s in the box is exactly 25%. (f) The percentage of 1’s in the box is around 25%, give or take 2% or so. 2. Complete the table for tossing a fair coin repeatedly. Number of tosses 100 2,500 10,000 1,000,000 Number of heads Expected value SE 50 Percent of heads Expected value SE 5% 3. A gym has about 2000 members, 60% of whom are younger than 50 and 40% of whom are 50 and above. The gym wants to know about the percentage of members who attend yoga classes, so they separately survey 120 people who are under 50, and 80 people who are 50 and above, choosing a simple random sample in each case. They then calculate the percentage of people in each of the samples who support the policy. Suppose the percentage of people who attend yoga is, in reality, the same in the two age groups. The accuracy of the estimate for the younger group will be (circle one) better than similar to worse than the accuracy of the estimate for the older group. Justify your answer. 5. Suppose the grade distribution of midterm scores in a large lecture course is as follows: 25% A, 30% B, 30% C, 10% D, 5% F The professor is going to sample 50 students at random from the class. Calculate the expected value and standard error for the percentage of students in the sample who got a C or better.