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Ch. 6 - Confidence Intervals
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Larson 8th EditionCh. 6 - Confidence Intervals문제 6.R.6
6장, 문제 6.R.6

In Exercises 5 and 6, use the confidence interval to find the margin of error and the sample mean.
(7.428, 7.562)

검증된 단계별 안내
1
Identify the given confidence interval, which is (7.428, 7.562). The confidence interval provides the range of plausible values for the population parameter.
To find the margin of error (ME), use the formula: ME = (Upper Limit - Lower Limit) / 2. Substitute the values from the confidence interval into this formula.
To find the sample mean, use the formula: Sample Mean = (Upper Limit + Lower Limit) / 2. Substitute the values from the confidence interval into this formula.
Perform the subtraction and division for the margin of error calculation, ensuring proper order of operations.
Perform the addition and division for the sample mean calculation, ensuring proper order of operations.

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주요 개념

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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. It is expressed as an interval (e.g., (7.428, 7.562)) and is associated with a confidence level, typically 95% or 99%, indicating the degree of certainty that the parameter lies within the interval.
추천 영상:
가이드 코스
06:33
Introduction to Confidence Intervals

Margin of Error

The margin of error quantifies the uncertainty in a sample estimate. It is calculated as half the width of the confidence interval, representing the maximum expected difference between the sample statistic and the population parameter. In this case, it can be found by subtracting the lower limit of the interval from the upper limit and dividing by two.
추천 영상:
가이드 코스
04:08
Finding the Minimum Sample Size Needed for a Confidence Interval

Sample Mean

The sample mean is the average of a set of sample observations and serves as a point estimate of the population mean. It can be calculated by taking the midpoint of the confidence interval, which provides a central value around which the interval is constructed. In this example, the sample mean can be found by averaging the two endpoints of the interval.
추천 영상:
가이드 코스
05:11
Sampling Distribution of Sample Proportion
관련 실천
교과서 질문

(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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교과서 질문

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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교과서 질문

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.

50
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교과서 질문

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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교과서 질문

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.

119
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교과서 질문

In Exercises 27–30, find the critical values and for the level of confidence c and sample size n.

c = 0.99, n = 10

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