question 8 ### Exercises 3–6: Normal Sampling DistributionDetermine whether a normal sampling distribution can be used. If it can be used, test the claim.3. **Claim:** $ p < 0.12 $; $ \alpha = 0.01 $. - **Sample statistics:** $ \hat{p} = 0.10 $, $ n = 40 $.4. **Claim:** $ p \geq 0.48 $; $ \alpha = 0.08 $. - **Sample statistics:** $ \hat{p} = 0.40 $, $ n = 90 $.5. **Claim:** $ p \neq 0.15 $; $ \alpha = 0.05 $. - **Sample statistics:** $ \hat{p} = 0.12 $, $ n = 500 $.6. **Claim:** $ p \geq 0.70 $; $ \alpha = 0.04 $. - **Sample statistics:** $ \hat{p} = 0.64 $, $ n = 225 $.### Using and Interpreting Concepts**Hypothesis Testing Using Rejection Regions**For Exercises 7–12, complete the following steps:- (a) Identify the claim and state $ H_0 $ and $ H_a $.- (b) Find the critical value(s) and identify the rejection region(s).- (c) Calculate the standardized test statistic $ z $.- (d) Decide whether to reject or fail to reject the null hypothesis.- (e) Interpret the decision in the context of the original claim.7. **Vaccination Requirement** A medical researcher says that less than 80% of U.S. adults think that healthy children should be required to be vaccinated. In a random sample of 200 U.S. adults, 82% think that healthy children should be vaccinated. At $ \alpha = 0.05 $, is there enough evidence to support the researcher's claim? (Adapted from Pew Research Center)8. **Internal Revenue Service Audits** A research center claims that at least 27% of U.S. adults think that the IRS will audit their taxes. In a random sample of 1000 U.S. adults in a recent year, 23% are concerned that the IRS will audit their taxes.

Name: question 8 ### Exercises 3–6: Normal Sampling DistributionDetermine wh
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Description: question 8 ### Exercises 3–6: Normal Sampling DistributionDetermine whether a normal sampling distribution can be used. If it can be used, test the claim.3. **Claim:** $ p < 0.12 $; $ \alpha = 0.01 $. - **Sample statistics:** \( \hat{p} = 0.10

Sample proportion = p^ = 23% = 0.23 Sample size = n = 1000 Null Hypothesis : H0 : p=0.27…

Math

Statistics

8. Internal Revenue Service Audits A research center claims that at least 27% of U.S. adults think that the IRS will audit their taxes. In a random sample of 1000 U.S. adults in a recent year, 23% say they are concerned that the IRS will audit their taxes. At a = 0.01, is there enough evidence to reject the center's claim? (Source: Rasmussen Reports)

8. Internal Revenue Service Audits A research center claims that at least 27% of U.S. adults think that the IRS will audit their taxes. In a random sample of 1000 U.S. adults in a recent year, 23% say they are concerned that the IRS will audit their taxes. At a = 0.01, is there enough evidence to reject the center's claim? (Source: Rasmussen Reports)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.

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question 8

### Exercises 3–6: Normal Sampling Distribution

Determine whether a normal sampling distribution can be used. If it can be used, test the claim.

3. **Claim:** $ p < 0.12 $; $ \alpha = 0.01 $.
- **Sample statistics:** $ \hat{p} = 0.10 $, $ n = 40 $.

4. **Claim:** $ p \geq 0.48 $; $ \alpha = 0.08 $.
- **Sample statistics:** $ \hat{p} = 0.40 $, $ n = 90 $.

5. **Claim:** $ p \neq 0.15 $; $ \alpha = 0.05 $.
- **Sample statistics:** $ \hat{p} = 0.12 $, $ n = 500 $.

6. **Claim:** $ p \geq 0.70 $; $ \alpha = 0.04 $.
- **Sample statistics:** $ \hat{p} = 0.64 $, $ n = 225 $.

### Using and Interpreting Concepts

**Hypothesis Testing Using Rejection Regions**

For Exercises 7–12, complete the following steps:
- (a) Identify the claim and state $ H_0 $ and $ H_a $.
- (b) Find the critical value(s) and identify the rejection region(s).
- (c) Calculate the standardized test statistic $ z $.
- (d) Decide whether to reject or fail to reject the null hypothesis.
- (e) Interpret the decision in the context of the original claim.

7. **Vaccination Requirement**

A medical researcher says that less than 80% of U.S. adults think that healthy children should be required to be vaccinated. In a random sample of 200 U.S. adults, 82% think that healthy children should be vaccinated. At $ \alpha = 0.05 $, is there enough evidence to support the researcher's claim?
(Adapted from Pew Research Center)

8. **Internal Revenue Service Audits**

A research center claims that at least 27% of U.S. adults think that the IRS will audit their taxes. In a random sample of 1000 U.S. adults in a recent year, 23% are concerned that the IRS will audit their taxes.

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