The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.17 and a simple random sample of 800 households will be selected from the population. Use the z-table. a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries. E(F) = (to 2 decimals) (to 4 decimals) b. What is the probability that the sample proportion will be within +0.02 of the population proportion (to 4 decimals)? c. Answer part (b) for a sample of 1600 households (to 4 decimals).
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = 0.17 and a simple random sample of 800 households will be selected from the population. Use the z-table. a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries. E(F) = (to 2 decimals) (to 4 decimals) b. What is the probability that the sample proportion will be within +0.02 of the population proportion (to 4 decimals)? c. Answer part (b) for a sample of 1600 households (to 4 decimals).
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
![**Problem Description:**
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is \( p = 0.17 \) and a simple random sample of 800 households will be selected from the population. Use the z-table.
**Tasks:**
a. Show the sampling distribution of \(\bar{p}\), the sample proportion of households spending more than $100 per week on groceries.
\[ E(\bar{p}) = \] (to 2 decimals)
\[ \sigma_{\bar{p}} = \] (to 4 decimals)
b. What is the probability that the sample proportion will be within ±0.02 of the population proportion (to 4 decimals)?
\[ \]
c. Answer part (b) for a sample of 1600 households (to 4 decimals).
\[ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37e2f913-30b2-4c8c-98d5-339163057ff1%2Faf11c594-865f-42d1-bd13-618800d1c3f2%2Fks8yps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is \( p = 0.17 \) and a simple random sample of 800 households will be selected from the population. Use the z-table.
**Tasks:**
a. Show the sampling distribution of \(\bar{p}\), the sample proportion of households spending more than $100 per week on groceries.
\[ E(\bar{p}) = \] (to 2 decimals)
\[ \sigma_{\bar{p}} = \] (to 4 decimals)
b. What is the probability that the sample proportion will be within ±0.02 of the population proportion (to 4 decimals)?
\[ \]
c. Answer part (b) for a sample of 1600 households (to 4 decimals).
\[ \]
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 3 steps with 3 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