Question

Your teacher prepares a large container full of colored beads. She claims that 1/8 of the beads are red, 1/4 are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher’s claim. The smallest number of beads you can take so that the conditions for performing inference are met is (a) 15 (b) 16 (c) 30 (d) 40 (e) 80

Name: Problem 22, Chapter 11: The Practice of Statistics for AP
Uploaded: 2020-09-18T13:07:51-08:00
Duration: 2 min
Channel: Allaa Ragai
Description: Your teacher prepares a large container full of colored beads. She claims that 1/8 of the beads are red, 1/4 are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher’s claim. The smallest number of beads you can take so that the conditions for performing inference are met is (a) 15 (b) 16 (c) 30 (d) 40 (e) 80

   Your teacher prepares a large container full of colored beads. She claims that 1/8 of the beads are red, 1/4 are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher’s claim. The smallest number of beads you can take so that the conditions for performing inference are met is
(a) 15
(b) 16
(c) 30
(d) 40
(e) 80

The Practice of Statistics for AP

Daren S. Starnes,… 4th Edition

Chapter 11, Problem 22

Instant Answer

Solved by Expert Allaa Ragai

09/18/2020

Step 1

We know that the sum of all probabilities has to be equal to 1. So, the probability of yellow beads is equal to 1 minus the probability of red beads minus the probability of blue beads. That is, $P_{yellow} = 1 - P_{red} - P_{blue} = 1 - \frac{1}{8} - \frac{1}{4} Show more…

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Your teacher prepares a large container full of colored beads. She claims that 1/8 of the beads are red, 1/4 are blue, and the remainder are yellow. Your class will take a simple random sample of beads from the container to test the teacher’s claim. The smallest number of beads you can take so that the conditions for performing inference are met is (a) 15 (b) 16 (c) 30 (d) 40 (e) 80

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Key Concepts

Simple Random Sampling

This is a sampling method where every member of the population has an equal chance of being selected for the sample. It ensures that the sample is representative of the population, reducing bias and allowing for valid inferences about population parameters.

Inference for Proportions

In statistical inference for proportions, we use sample data to draw conclusions about the population proportion. This process typically involves checking that the sample is sufficiently large so that the sampling distribution of the proportion is approximately normal, using conditions such as np and n(1-p).

Expected Count Conditions (np and n(1-p) ? 10)

To use the normal approximation for the distribution of a sample proportion, it is generally required that both np and n(1-p) are at least 10. This ensures that there are enough expected successes and failures for the approximation to be valid, a critical requirement for performing reliable inference.

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