Domanda del libro di testo
(a) Construct a 90% confidence interval for the population mean in Exercise 1. Interpret the results. (b) Does it seem likely that the population mean could be within 10% of the sample mean? Explain.
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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.23
In Exercise 19, would it be unusual for the population proportion to be 38%? Explain.
Guida verificata passo dopo passo1
Step 1: Identify the given population proportion (p) from the problem. Here, the population proportion is 38%, which can be written as p = 0.38.
Step 2: Determine the context of 'unusual' in statistics. Typically, an event is considered unusual if it lies more than 2 standard deviations away from the mean in a normal distribution.
Step 3: Calculate the standard error (SE) of the population proportion using the formula: , where p is the population proportion and n is the sample size. If the sample size (n) is not provided, it must be specified to proceed.
Step 4: Use the calculated standard error to determine the range of usual values. The range is given by: . This range represents the interval within which values are considered usual.
Step 5: Compare the given population proportion (38%) to the calculated range. If 38% lies outside this range, it would be considered unusual. Otherwise, it is not unusual.
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Population Proportion
Population proportion refers to the fraction of a population that possesses a certain characteristic. It is a key parameter in statistics, often denoted as 'p', and is used to make inferences about the entire population based on sample data. Understanding the population proportion helps in determining the likelihood of observing certain outcomes in a sample.
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Percorso guidato
05:45
Constructing Confidence Intervals for Proportions
Statistical Significance
Statistical significance assesses whether the observed data deviates from what would be expected under a null hypothesis. In the context of population proportions, a proportion of 38% may be evaluated against a hypothesized value to determine if it is statistically unusual. This involves hypothesis testing and calculating p-values to draw conclusions about the population.
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Percorso guidato
05:53Parameters vs. Statistics
Confidence Intervals
A confidence interval provides a range of values within which the true population proportion is likely to fall, based on sample data. It reflects the uncertainty associated with estimating the population parameter. If the 38% proportion lies outside the confidence interval, it may suggest that this value is unusual or not representative of the population.
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06:33Introduction to Confidence Intervals
Pratica correlata
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In a random sample of 36 top-rated roller coasters, the average height is 165 feet and the standard deviation is 67 feet. Construct a 90% confidence interval for μ. Interpret the results. (Source: POP World Media, LLC)
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Domanda del libro di testo
Determine the minimum sample size required to be 99% confident that the sample mean driving distance to work is within 2 miles of the population mean driving distance to work. Use the population standard deviation from Exercise 2.
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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.
b. Find the minimum sample size needed, using a prior study that found that 32% of U.S. adults have taken or planned to take a winter vacation in a recent year. (Source: Rasmussen Reports)
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Domanda del libro di testo
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 73,901 college graduates, 23,991 obtained a postgraduate degree. (Adapted from Gallup)
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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 = 0.90, s = 25.6, n = 16, xbar = 72.1
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