Domanda del libro di testo
Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics.
c = 0.88
101
views
Ch. 6 - Confidence Intervals
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Capitolo 6, Problema 6.1.29
In Exercises 29–32, determine the minimum sample size n needed to estimate for the values of c, σ, and E.
c = 0.90, σ = 6.8, E = 1.
Guida verificata passo dopo passo1
Identify the formula for determining the minimum sample size n for estimating a population mean: , where zc is the critical z-value, σ is the population standard deviation, and E is the margin of error.
Determine the critical z-value (zc) for the given confidence level c = 0.90. Use a z-table or statistical software to find the z-value corresponding to the middle 90% of the standard normal distribution.
Substitute the given values into the formula: σ = 6.8 and E = 1. Replace zc with the critical z-value obtained in the previous step.
Simplify the fraction by multiplying zc and σ, then dividing by E.
Square the result of the fraction to compute the minimum sample size n. If n is not a whole number, always round up to the nearest integer, as sample size must be an integer.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Sample Size Determination
Sample size determination is the process of calculating the number of observations or replicates needed in a statistical study to ensure that the results are reliable and valid. It is crucial for achieving a desired level of confidence and margin of error in estimates. The formula often used involves the population standard deviation, the desired confidence level, and the margin of error.
Video consigliato:
Percorso guidato
06:14
Coefficient of Determination
Confidence Level (c)
The confidence level represents the probability that the confidence interval will contain the true population parameter. A confidence level of 0.90 indicates that there is a 90% chance that the interval estimate will capture the true value. This level influences the width of the confidence interval and, consequently, the required sample size.
Video consigliato:
Percorso guidato
06:33Introduction to Confidence Intervals
Margin of Error (E)
The margin of error is the range within which the true population parameter is expected to lie, given a certain confidence level. It quantifies the uncertainty associated with sample estimates. A smaller margin of error requires a larger sample size, as it indicates a desire for more precise estimates of the population parameter.
Video consigliato:
Percorso guidato
06:33Introduction to Confidence Intervals
Pratica correlata
Domanda del libro di testo
In Exercises 13 and 14, use the confidence interval to find the margin of error and the sample mean.
(14.7, 22.1)
95
views
Domanda del libro di testo
Translating Statements In Exercises 29–34, translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 220 U.S. adults ages 18–29, 65% said that they use Snapchat. The survey’s margin of error is ±7.9%. (Source: Pew Research Center)
73
views
Domanda del libro di testo
In Exercises 35–40, use the standard normal distribution or the t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results.
In a random sample of 18 months from January 2011 through December 2020, the mean interest rate for 30-year fixed rate home mortgages was 3.95% and the standard deviation was 0.49%. Assume the interest rates are normally distributed. (Source: Freddie Mac)
101
views
Domanda del libro di testo
Translating Statements In Exercises 29–34, translate the statement into a confidence interval. Approximate the level of confidence.
In a survey of 1000 U.S. adults, 71% think teaching is one of the most important jobs in our country today. The survey’s margin of error is ±3%. (Source: Rasmussen Reports)
88
views
Domanda del libro di testo
Finding Critical Values for χ2 In Exercises 3–8, find the critical values χR2 and χL2 for the level of confidence c and sample size n.
c = 0.80, n = 51
61
views