Directions: Solve the following problems to determine the sample size. A Senior High School teacher wants to estimate the average number of hours his working students work per week. The standard deviation from previous study is 3.2 hours. How large a sample must be selected if he wants to be accurate within 3% of the true proportion. be 99% confident of finding whether the true mean differsWhat sample size does he need? | from the sample mean by 1 hour? Solution: Since o = 3.2, 99% confidence, and E = 1, then Rodel wants to know, with 95% confidence, the proportion of students who play Mobile Legends (ML). A previous study showed that 46% play ML. Rodel wants to Solution: Note that q' = 1 – p =1- 0.46 = 0.54 Since E = 0.03, p = 0.46, q = 0.54, and confidence level is 95%, then n = E [(2.58)(3.2) n = pq (A E 1 (1.96\ n = 68.16 or 69 n = (0.56)(0.54)( Therefore, to be 99% confident that the estimate differs | from the true mean by 1 hour, the teacher needs a sample size of at least 69 working students. (0.03, n = 1290.78 or 1291 Thus, Rodel needs a sample of 1291 students. Activity. Find the sample size of each of the following: 1. 90% confidence, o = 25, E = 3 2. 98% confidence, E = 2.6, p= 0.37
Directions: Solve the following problems to determine the sample size. A Senior High School teacher wants to estimate the average number of hours his working students work per week. The standard deviation from previous study is 3.2 hours. How large a sample must be selected if he wants to be accurate within 3% of the true proportion. be 99% confident of finding whether the true mean differsWhat sample size does he need? | from the sample mean by 1 hour? Solution: Since o = 3.2, 99% confidence, and E = 1, then Rodel wants to know, with 95% confidence, the proportion of students who play Mobile Legends (ML). A previous study showed that 46% play ML. Rodel wants to Solution: Note that q' = 1 – p =1- 0.46 = 0.54 Since E = 0.03, p = 0.46, q = 0.54, and confidence level is 95%, then n = E [(2.58)(3.2) n = pq (A E 1 (1.96\ n = 68.16 or 69 n = (0.56)(0.54)( Therefore, to be 99% confident that the estimate differs | from the true mean by 1 hour, the teacher needs a sample size of at least 69 working students. (0.03, n = 1290.78 or 1291 Thus, Rodel needs a sample of 1291 students. Activity. Find the sample size of each of the following: 1. 90% confidence, o = 25, E = 3 2. 98% confidence, E = 2.6, p= 0.37
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
Related questions
Question
Transcribed Image Text:Directions: Solve the following problems to determine the sample size.
A Senior High School teacher wants to estimate the
Rodel wants to know, with 95% confidence, the
average number of hours his working students work per
proportion of students who play Mobile Legends (ML). A
week. The standard deviation from previous study is 3.2
previous study showed that 46% play ML. Rodel wants to
hours. How large a sample must be selected if he wants to be accurate within 3% of the true proportion.
be 99% confident of finding whether the true mean differs What sample size does he need?
from the sample mean by 1 hour?
Solution:
Note that q = 1 - p=1 – 0.46 = 0.54 Since E =
0.03, p = 0.46, q = 0.54, and confidence level is
|95%, then
Solution: Since o= 3.2, 99% confidence, and
E = 1, then
(za/2
n =
za/2
2
E
[(2.58)(3.2)|²
n = pq
E
2
1
(1.96v
n = (0.56)(0.54)|
n = 68.16 or 69
Therefore, to be 99% confident that the estimate differs
from the true mean by 1 hour, the teacher needs a sample
size of at least 69 working students.
(0.03)
n = 1290.78 or 1291
Thus, Rodel needs a sample of 1291 students.
Activity.
Find the sample size of each of the following:
1. 90% confidence, o = 25, E = 3
2. 98% confidence, E = 2.6, p= 0.37
3.
Yellow Bus Lines, Inc. wants to know the amount of time it takes its bus to travel from one bus stop to the next.
From the past observations, the standard deviation is 25 minutes. How many samples are needed in order to be 98% sure
that that the maximum error of estimate is 5 minutes?
4.
You want to know the average number of hours a student spends each day in watching Korean Drama Series. The
standard deviation from previous study is 3.7 hours. How large a sample must be selected if you wants to be 95% confident
of finding whether the true mean differs from the sample mean by half an hour?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON