Domanda del libro di testo
Graphical Analysis In Exercises 9–12, use the values on the number line to find the sampling error.
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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 6.3.12
Constructing Confidence Intervals In Exercises 11 and 12, construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.
New Year’s Resolutions In a survey of 1790 U.S. adults in a recent year, 816 have a New Year’s resolution related to their health. (Adapted from Finder)
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Step 1: Identify the sample proportion (p̂) and the sample size (n). The sample proportion is calculated as p̂ = x / n, where x is the number of successes (816) and n is the total sample size (1790).
Step 2: Determine the critical z-scores for the desired confidence levels. For a 90% confidence interval, the critical z-score is approximately 1.645. For a 95% confidence interval, the critical z-score is approximately 1.96.
Step 3: Calculate the standard error (SE) of the sample proportion using the formula SE = sqrt((p̂ * (1 - p̂)) / n).
Step 4: Construct the confidence intervals using the formula: CI = p̂ ± (z * SE), where z is the critical z-score for the desired confidence level. Perform this calculation separately for the 90% and 95% confidence levels.
Step 5: Compare the widths of the confidence intervals. The width of a confidence interval is given by 2 * (z * SE). Note that the 95% confidence interval will be wider than the 90% confidence interval because a higher confidence level requires a larger margin of error.
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Confidence Interval
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence, such as 90% or 95%. It provides an estimate of uncertainty around the sample proportion, indicating how much the sample result might vary if different samples were taken.
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06:33
Introduction to Confidence Intervals
Population Proportion
The population proportion is the ratio of members of a population that have a particular characteristic, expressed as a fraction or percentage. In this context, it refers to the proportion of U.S. adults who have a New Year’s resolution related to their health, which is estimated from the sample data.
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05:45Constructing Confidence Intervals for Proportions
Width of Confidence Intervals
The width of a confidence interval reflects the precision of the estimate; narrower intervals indicate more precise estimates of the population parameter. The width is influenced by the sample size and the confidence level chosen; higher confidence levels result in wider intervals, while larger sample sizes yield narrower intervals, allowing for more accurate estimates.
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06:33Introduction to Confidence Intervals
Pratica correlata
Domanda del libro di testo
In Exercises 5–8, find the critical value zc necessary to construct a confidence interval at the level of confidence c.
c = 0.80
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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 = 0.95, n = 20
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Domanda del libro di testo
You research prices of cell phones and find that the population mean is \$431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95?
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Domanda del libro di testo
Finding p^ and q^ In Exercises 3–6, let p be the population proportion for the situation. Find point estimates of p and q.
Private Internet Browsing In a survey of 4272 U.S. adults, 1025 knew that private browsing mode only prevents someone using the same computer from seeing one’s online activities. (Adapted from Pew Research Center)
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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.
The population standard deviation of the weights of the two-year-old males on a pediatrician’s patient list is 2.49 pounds. The mean weight of a sample of 10 of the two–year–old males is 13.68 pounds. Weights are known to be normally distributed.
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