Domanda del libro di testo
In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.
c = 0.95, n = 13
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Ch. 6 - Confidence Intervals
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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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.R.25a
You wish to estimate, with 95% confidence, the population proportion of U.S. adults who have taken or planned to take a winter vacation in a recent year. Your estimate must be accurate within 5% of the population proportion.
a. No preliminary estimate is available. Find the minimum sample size needed.
Guida verificata passo dopo passo1
Determine the formula for the minimum sample size needed to estimate a population proportion with a given margin of error. The formula is: , where is the z-score corresponding to the confidence level, is the estimated population proportion, and is the margin of error.
Since no preliminary estimate of the population proportion is available, use (or 0.5). This value maximizes the product , ensuring the sample size is large enough.
Identify the z-score corresponding to a 95% confidence level. For a 95% confidence level, the z-score is approximately 1.96. This value is derived from the standard normal distribution.
Set the margin of error to 0.05 (5%). This is the desired level of accuracy for the estimate.
Substitute the values into the formula: . Simplify the expression to calculate the minimum sample size needed.
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Population Proportion
The population proportion refers to the fraction of a population that possesses a certain characteristic, in this case, U.S. adults who have taken or planned to take a winter vacation. It is denoted by 'p' and is crucial for estimating how widespread a behavior or opinion is within a population.
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05:45
Constructing Confidence Intervals for Proportions
Sample Size Calculation
Sample size calculation is a statistical method used to determine the number of observations or replicates needed to ensure that the results of a study are statistically valid. In this context, it involves using the desired confidence level and margin of error to find the minimum number of respondents required to accurately estimate the population proportion.
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05:11Sampling Distribution of Sample Proportion
Confidence Interval
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the population parameter with a specified level of confidence, such as 95%. It reflects the uncertainty associated with estimating the population proportion and is influenced by the sample size and variability in the data.
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06:33Introduction to Confidence Intervals
Pratica correlata
Domanda del libro di testo
In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.
c = 0.98, n = 25
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Domanda del libro di testo
In Exercises 13–16, (a) find the margin of error for the values of c, s, and n, and (b) construct the confidence interval for using the t-distribution. Assume the population is normally distributed.
c = 0.98, s = 0.9, n = 12, xbar = 6.8
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Domanda del libro di testo
In Exercises 5 and 6, use the confidence interval to find the margin of error and the sample mean.
(7.428, 7.562)
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In Exercises 19–22, let p be the population proportion for the situation. (a) Find point estimates of p and q, (b) construct 90% and 95% confidence intervals for p, and (c) interpret the results of part (b) and compare the widths of the confidence intervals.
In a survey of 912 U.S. adults in Generation Z (born after 1996), 383 said they are at least somewhat likely to consider an electric vehicle for their next vehicle purchase. (Adapted from Pew Research Center)
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Domanda del libro di testo
In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.
c = 0.99, n = 10
97
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