Textbook Question
Happiness In a survey sponsored by Coca-Cola, subjects were asked what contributes most to their happiness, and the table summarizes their responses. Does the table represent a probability distribution? Explain.
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Ch. 5 - Discrete Probability Distributions
Triola14th EditionElementary StatisticsISBN: 9780137366446
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Table of contents
- 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
Chapter 5, Problem 5.2.29c
In Exercises 29 and 30, assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XSORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.
Gender Selection Assume that the groups consist of 36 couples.
c. Is the result of 26 girls a result that is significantly high? What does it suggest about the effectiveness of the XSORT method?
Verified step by step guidance1
Step 1: Define the problem in terms of a binomial distribution. The number of trials (n) is 36 (the number of couples), the probability of success (p) is 0.5 (probability of having a girl), and the number of successes (x) is 26 (number of girls).
Step 2: Calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the formulas: μ = n * p and σ = √(n * p * (1 - p)).
Step 3: Determine the threshold for a 'significantly high' result. A result is considered significantly high if it is greater than μ + 2σ. Compute this threshold using the values of μ and σ from Step 2.
Step 4: Compare the observed value (26 girls) to the threshold calculated in Step 3. If 26 is greater than μ + 2σ, it is considered significantly high.
Step 5: Interpret the result. If the result is significantly high, it suggests that the XSORT method may have an effect. If it is not significantly high, it suggests that the XSORT method may not be effective.
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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 having a girl is 0.5, meaning there is an equal chance of having a boy or a girl. Understanding probability is essential for determining whether the observed outcome of 26 girls out of 36 births is statistically significant.
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Statistical Significance
Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere random chance. In this scenario, we need to assess whether the occurrence of 26 girls is significantly higher than what would be expected by chance alone, given a 50% probability for each gender. This involves comparing the observed result to a theoretical distribution of outcomes.
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05:53Parameters vs. Statistics
Binomial Distribution
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. In this case, the number of girls born can be modeled using a binomial distribution with parameters n = 36 (the number of couples) and p = 0.5 (the probability of having a girl). This distribution helps in calculating the probability of observing 26 girls and determining if it is an unusual outcome.
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Related Practice
Textbook Question
Using Probabilities for Significant Events
c. Which probability is relevant for determining whether 3 is a significantly high number of matches: the result from part (a) or part (b)?
Textbook Question
Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.
b. Among those who negotiated salary, 84% received higher pay. How many received higher pay?
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Textbook Question
In Exercises 25–28, find the probabilities and answer the questions.
Internet Voting Based on a Consumer Reports survey, 39% of likely voters would be willing to vote by Internet instead of the in-person traditional method of voting. For each of the following, assume that 15 likely voters are randomly selected.
c. Find the probability that at least one of the selected likely voters would do Internet voting.
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Textbook Question
Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.
0 0 1 2 17 28 21 8
e. Find the standard deviation.
f. Find the variance.
Textbook Question
Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.
a. 29% of the respondents reported that they negotiated salary at their latest job. What is the number of respondents who reported that they negotiated salary?
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