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Ch. 8 - Hypothesis Testing
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 8 - Hypothesis TestingProblem 8.c.8a
Chapter 8, Problem 8.c.8a

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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1
Identify the given probability of a single event: The probability that a randomly selected lightning death victim is male is given as P(Male) = 0.8.
Recognize that the problem involves finding the probability of three independent events occurring. Since the gender of each victim is independent of the others, the probability of all three being male can be calculated using the multiplication rule for independent events.
Write the formula for the probability of three independent events: P(All males) = P(Male) × P(Male) × P(Male).
Substitute the given probability into the formula: P(All males) = 0.8 × 0.8 × 0.8.
Simplify the expression to find the final probability, but do not calculate the numerical result in this step.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, the probability of an event, such as a lightning death being male, is given as 0.8. This means there is an 80% chance that a randomly selected lightning death victim is male.
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Introduction to Probability

Independent Events

Independent events are those whose outcomes do not affect each other. In this scenario, the deaths of three individuals by lightning strikes can be considered independent events, meaning the gender of one victim does not influence the gender of another. This allows us to multiply the probabilities of each event occurring to find the overall probability.
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Probability of Multiple Independent Events

Multiplication Rule of Probability

The multiplication rule of probability states that the probability of multiple independent events occurring together is the product of their individual probabilities. For this question, to find the probability that all three randomly selected lightning death victims are male, we multiply the probability of one male victim (0.8) by itself three times, resulting in 0.8^3.
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Probability of Multiple Independent Events
Related Practice
Textbook Question

Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.

46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20

d. Variance

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Textbook Question

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.

105
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Textbook Question

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.

133
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Textbook Question

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


c. For the hypothesis test, identify the value used for the population proportion and use the symbol that represents it.

111
views
Textbook Question

Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.

46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20

c. standard deviation

118
views
Textbook Question

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.

104
views