Domanda del libro di testo
Claim of “At Least” or “At Most”
How do the following results change?
a. Chapter Problem claim is changed to this: “At least 50% of Internet users utilize two-factor authentication to protect their online data.”
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Ch. 8 - Hypothesis Testing
Triola14th EditionElementary StatisticsISBN: 9780137366446
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TOC.tableOfContents
- Ch. 1 - Introduction to Statistics88
- Ch. 2 - Exploring Data with Tables and Graphs70
- Ch. 3 - Describing, Exploring, and Comparing Data66
- Ch. 4 - Probability112
- Ch. 5 - Discrete Probability Distributions109
- Ch. 6 - Normal Probability Distributions122
- Ch. 7 - Estimating Parameters and Determining Sample Sizes107
- Ch. 8 - Hypothesis Testing75
- Ch. 9 - Inferences from Two Samples94
- Ch. 10 - Correlation and Regression80
- Ch. 11 - Goodness-of-Fit and Contingency Tables29
- Ch. 12 - Analysis of Variance42
Triola14th EditionElementary StatisticsISBN: 9780137366446Non è quello che usi tu?Cambia libro di testo
Capitolo 8, Problema 8.2.1b
Statistical Literacy and Critical Thinking
In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.
Number and Proportions
b. Identify the sample proportion and use the symbol that represents it.
Guida verificata passo dopo passo1
Step 1: Understand the problem. The goal is to identify the sample proportion from the given data and use the appropriate statistical symbol to represent it. The sample proportion is the ratio of respondents who rated themselves as above average drivers to the total number of respondents.
Step 2: Recall the formula for sample proportion. The sample proportion (denoted as ) is calculated as: , where is the number of respondents who rated themselves as above average drivers, and is the total sample size.
Step 3: Extract the values from the problem. The total sample size is , and the percentage of respondents who rated themselves as above average drivers is . Convert this percentage to a proportion by dividing by 100: .
Step 4: Calculate the number of respondents who rated themselves as above average drivers. Multiply the proportion () by the total sample size (): .
Step 5: Substitute the values into the formula for sample proportion. Use to represent the sample proportion, where is the number of respondents calculated in Step 4 and is .
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Sample Proportion
The sample proportion is a statistic that represents the fraction of a sample that possesses a certain characteristic. It is calculated by dividing the number of individuals in the sample with the characteristic by the total number of individuals in the sample. In this case, the sample proportion of adults who rate themselves as above average drivers can be expressed as 0.86, or 86%, based on the survey results.
Video consigliato:
Percorso guidato
05:11
Sampling Distribution of Sample Proportion
Hypothesis Testing
Hypothesis testing is a statistical method used to make inferences about a population based on sample data. It involves formulating a null hypothesis (the default assumption) and an alternative hypothesis (the claim being tested). In this scenario, the null hypothesis would state that 75% or fewer adults rate themselves as above average drivers, while the alternative hypothesis would assert that more than 75% do.
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Percorso guidato
06:21Step 1: Write Hypotheses
Simple Random Sample
A simple random sample is a subset of individuals chosen from a larger population in such a way that every individual has an equal chance of being selected. This method helps ensure that the sample is representative of the population, reducing bias in the results. In the context of the survey, the 1020 adults surveyed were selected randomly, which supports the validity of the conclusions drawn from the sample.
Video consigliato:
Percorso guidato
05:11Sampling Distribution of Sample Proportion
Pratica correlata
Domanda del libro di testo
Statistical Literacy and Critical Thinking
In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.
Null and Alternative Hypotheses and Test Statistic
a. Identify the null hypothesis and the alternative hypothesis.
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Domanda del libro di testo
Statistical Literacy and Critical Thinking
In Exercises 1–4, use the results from a Hankook Tire Gauge Index survey of a simple random sample of 1020 adults. Among the 1020 respondents, 86% rated themselves as above average drivers. We want to test the claim that more than 3/4 of adults rate themselves as above average drivers.
Null and Alternative Hypotheses and Test Statistic
b. Find the value of the test statistic.
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Domanda del libro di testo
At Least As Extreme A random sample of 860 births in New York State included 426 boys, and that sample is to be used for a test of the common belief that the proportion of male births in the population is equal to 0.512.
b. For random samples of size 860, what sample proportions of male births are at least as extreme as the sample proportion of 426/860?
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Domanda del libro di testo
Using Confidence Intervals to Test Hypotheses When analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.
b. Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.
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Domanda del libro di testo
Lightning Deaths Based on the results given in Cumulative Review Exercise 6, assume that for a randomly selected lightning death, there is a 0.8 probability that the victim is a male.
a. Find the probability that three random people killed by lightning strikes are all males.
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