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Ch. 5 - Discrete Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 5 - Discrete Probability DistributionsProblem 5.1.28
Chapter 5, Problem 5.1.28

Stem Cell Survey In a Newsweek poll of 882 adults, 481 (or 55%) said that they were in favor of using federal tax money to fund medical research using stem cells obtained from human embryos. A politician claims that people don’t really understand the stem cell issue and their responses to such questions are random responses equivalent to a coin toss. Use the following probabilities related to determining whether the result of 481 is significantly high (assuming the true rate is 50%). Is 481 significantly high? What should be concluded about the politician’s claim? Explain.


P(respondent says to use the federal tax money) = 0.5
P(among 882, exactly 481 says to use federal tax money) = 0.000713
P(among 882,481 or more say to use federal tax money) = 0.00389

Verified step by step guidance
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Step 1: Define the null hypothesis (H0) and alternative hypothesis (H1). The null hypothesis assumes that the responses are random and equivalent to a coin toss, meaning the true proportion of people in favor is 0.5. The alternative hypothesis suggests that the proportion is significantly different from 0.5.
Step 2: Identify the given probabilities and their relevance. The problem provides P(respondent says to use federal tax money) = 0.5, P(among 882, exactly 481 says to use federal tax money) = 0.000713, and P(among 882, 481 or more say to use federal tax money) = 0.00389. The last probability, P(481 or more), is the cumulative probability used to determine if the observed result is significantly high.
Step 3: Determine the significance level (α). Typically, a significance level of 0.05 is used unless otherwise specified. Compare the cumulative probability P(481 or more) = 0.00389 to the significance level. If this probability is less than α, the result is considered significantly high.
Step 4: Interpret the result. Since P(481 or more) = 0.00389 is less than 0.05, the observed result of 481 respondents in favor is significantly high. This suggests that the responses are not random and are unlikely to be equivalent to a coin toss.
Step 5: Conclude about the politician’s claim. Based on the statistical evidence, the claim that people’s responses are random and equivalent to a coin toss is not supported. The data indicates that there is a significant preference among respondents in favor of using federal tax money for stem cell research.

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Key Concepts

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

Hypothesis Testing

Hypothesis testing is a statistical method used to determine whether there is enough evidence to reject a null hypothesis. In this context, the null hypothesis would state that the proportion of adults in favor of funding stem cell research is 50%. By comparing the observed result (481 supporters) to the expected result under the null hypothesis, we can assess whether the observed data is statistically significant.
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Step 1: Write Hypotheses

P-Value

The p-value is a measure that helps determine the significance of the results obtained in a statistical test. It represents the probability of observing a result as extreme as, or more extreme than, the one obtained, assuming the null hypothesis is true. In this case, the p-value of 0.00389 indicates a very low probability of obtaining 481 or more supporters if the true proportion is indeed 50%, suggesting that the result is statistically significant.
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Step 3: Get P-Value

Statistical Significance

Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere random chance. A common threshold for significance is a p-value of less than 0.05. Given the p-value of 0.00389 in this scenario, we can conclude that the proportion of supporters (481) is significantly higher than what would be expected by random chance, challenging the politician's claim that responses are random.
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Parameters vs. Statistics
Related Practice
Textbook Question

Texting and Driving. In Exercises 21–26, refer to the accompanying table, which describes probabilities for groups of five drivers. The random variable x is the number of drivers in a group who say that they text while driving (based on data from an Arity survey of drivers).

Using Probabilities for Significant Events


a. Find the probability of getting exactly 3 drivers who say that they text while driving.


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Textbook Question

40% of consumers believe that cash will be obsolete in the next 20 years (based on a survey by J.P. Morgan Chase). In each of Exercises 15–20, assume that 8 consumers are randomly selected. Find the indicated probability.


Find the probability that at least 6 of the selected consumers believe that cash will be obsolete in the next 20 years.

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Textbook Question

40% of consumers believe that cash will be obsolete in the next 20 years (based on a survey by J.P. Morgan Chase). In each of Exercises 15–20, assume that 8 consumers are randomly selected. Find the indicated probability.


Find the probability that exactly 6 of the selected consumers believe that cash will be obsolete in the next 20 years.

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Textbook Question

For the distribution described in Exercise 1, find the probability of exactly 2 arrivals in one thousandth of a minute.

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Textbook Question

In Exercises 5–12, determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). For those that are not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.


Pew Survey In a Pew Research Center survey of 3930 subjects, the ages of the respondents are recorded.

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Textbook Question

In Exercises 5–12, determine whether the given procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). For those that are not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.


In a Pew Research Center survey, 3930 subjects were asked if they have ever fired a gun, and the responses consist of “yes” or “no.”

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