A random sample of 1026 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1026 adults surveyed, 515 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without. p= 0.502 (Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample Va simple random sample, the value of is. which is V 10, and the V less than or equal to 5% of the (Round to three decimal places as needed.)
A random sample of 1026 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1026 adults surveyed, 515 indicated that televisions are a luxury they could do without. Complete parts (a) through (e) below. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without. p= 0.502 (Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample Va simple random sample, the value of is. which is V 10, and the V less than or equal to 5% of the (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:**Standard Normal Distribution Table**
The standard normal distribution table, also known as the Z-table, helps us find the probability that a statistic is observed below, above, or between values on the standard normal distribution.
**Page 1:**
- **Diagram**: The graph shows a bell-shaped normal distribution curve, highlighting the area under the curve to the left of a specific Z-value (z). This shaded area represents the probability of a random variable falling below that Z-value.
- **Table**:
- The table is structured in rows and columns.
- The first column lists Z-values from -3.4 to -0.1 in increments of 0.1.
- The subsequent columns correspond to Z-value decimals from 0.00 to 0.09.
- Each table entry represents the cumulative probability from the mean (0) to the Z-value specified by combining the row and column values.
**Z-value and probability examples from Page 1:**
- Z = -3.4 and decimal 0.00: Probability is 0.0003
- Z = -1.5 and decimal 0.05: Probability is 0.0668
- Z = -0.3 and decimal 0.09: Probability is 0.3707
**Page 2:**
- **Diagram**: Similar bell-shaped curve as Page 1, highlighting the cumulative probability area.
- **Table**:
- Continues from Page 1 with Z-values ranging from 0.0 to 3.8.
- Format remains the same, with the first column listing the Z-values and additional columns indicating the decimal places.
**Z-value and probability examples from Page 2:**
- Z = 0.0 and decimal 0.02: Probability is 0.5080
- Z = 1.8 and decimal 0.07: Probability is 0.9649
- Z = 2.5 and decimal 0.09: Probability is 0.9938
**Usage**: This table is useful in statistics for determining probabilities for normal distribution, which is widely used in fields such as psychology, finance, and natural sciences.
- [Page 2 of the Standard Normal Distribution Table](#)
**Analysis and Calculations**
*(a) Obtain a Point Estimate:*
- The point estimate for the population proportion (\(\hat{p}\)) of adults who believe televisions are a luxury is 0.502.
- Note: Round to three decimal places as needed.
*(b) Validate Confidence Interval Requirements:*
- Confirm the sample is a simple random sample.
- Calculate the value of \(\hat{p}\) as a reminder:
\(\hat{p}\) = 0.502.
- Ensure that \(np\) and \(n(1-p)\) are both greater than or equal to 10.
- Verify that the sample is less than or equal to 5% of the total population.
- Round to three decimal places as necessary during calculations for precise results.
Please use the fields provided to input your own calculations and verify them to gain a deeper understanding of the process involved in survey data analysis and inference regarding population proportions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3687cbc-fe37-486e-87e6-a5fec1076243%2F33ea46f5-a06a-4f4b-8560-a5554e8ec3cb%2F9d1g8r_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
---
**Survey Analysis on Television Necessity**
A random sample of 1,026 adults in a large country was surveyed with the question: "Do you pretty much think televisions are a necessity or a luxury you could do without?" Among those surveyed, 515 adults indicated that televisions are a luxury they could do without. The analysis below breaks down the data and examines the statistical requirements for constructing a confidence interval.
**Standard Normal Distribution Tables**
To assist with further analysis, you may need to refer to the standard normal distribution tables:
- [Page 1 of the Standard Normal Distribution Table](#)
- [Page 2 of the Standard Normal Distribution Table](#)
**Analysis and Calculations**
*(a) Obtain a Point Estimate:*
- The point estimate for the population proportion (\(\hat{p}\)) of adults who believe televisions are a luxury is 0.502.
- Note: Round to three decimal places as needed.
*(b) Validate Confidence Interval Requirements:*
- Confirm the sample is a simple random sample.
- Calculate the value of \(\hat{p}\) as a reminder:
\(\hat{p}\) = 0.502.
- Ensure that \(np\) and \(n(1-p)\) are both greater than or equal to 10.
- Verify that the sample is less than or equal to 5% of the total population.
- Round to three decimal places as necessary during calculations for precise results.
Please use the fields provided to input your own calculations and verify them to gain a deeper understanding of the process involved in survey data analysis and inference regarding population proportions.
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
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman