# In a recent statewide election. 55% of the voters rejected a proposal to institute a state lottery. In a random sample of 150 urban precincts, 49% of the voters rejected the proposal. Is the difference significant? Summarize your conclusions in a sentence or two.

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 7, Problem 7.13P
Textbook Problem
305 views

## In a recent statewide election. 55% of the voters rejected a proposal to institute a state lottery. In a random sample of 150 urban precincts, 49% of the voters rejected the proposal. Is the difference significant? Summarize your conclusions in a sentence or two.

Expert Solution
To determine

To find:

The significant difference between the given statements.

### Explanation of Solution

Given:

The given information is,

In a recent statewide election. 55% of the voters rejected a proposal to institute a state lottery. In a random sample of 150 urban precincts, 49% of the voters rejected the proposal.

The five step model for hypothesis testing is:

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For large samples with single sample proportions, the Z value is given by,

Z(obtained)=PsPuPu(1Pu)/N

Where, Ps is the sample proportion,

Pu is the population proportion and,

N is the sample size.

Calculation:

From the given information, the sample size is 150, sample proportion is 49% and the population proportion is 55%.

Follow the steps for two-tailed hypothesis testing as,

Step 1. Making assumptions and meeting test requirements.

Model:

Random sampling.

Level of measurement is interval ratio.

Sampling distribution is Normal.

Step 2. Stating the null hypothesis.

The statement of the null hypothesis is that the proportion of voters from the sample who rejected the proposal are not significantly different from the proportion of voters from the population who rejected the proposal.

Thus, the null and the alternative hypotheses are,

H0:Pu=0.55

H1:Pu0.55

Step 3. Selecting the sampling distribution and establishing the critical region.

Since, the sample is large, Z distribution can be used.

The information given is in the form of proportions, the test for proportion can be used.

Thus, the sampling distribution is Z distribution.

The level of significance is α=0.05.

And area of critical region is Z(critical)=±1

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The text passage describes a statistical hypothesis testing problem where the goal is to determine if there is a significant difference between the proportion of voters who rejected a state lottery proposal in a statewide election (55%) and a random sample of 150 urban precincts (49%).
no_question

the passage does not contain a direct mathematical question or calculation request. instead, it provides a context for a statistical hypothesis test and outlines the steps to perform the test. the "question" is implicitly about whether the difference in proportions is statistically significant, but it is not phrased as a direct question. the passage also does not provide a specific answer to this implicit question.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# In a recent statewide election. 55% of the voters rejected a proposal to institute a state lottery. In a random sample of 150 urban precincts, 49% of the voters rejected the proposal. Is the difference significant? Summarize your conclusions in a sentence or two.

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 7, Problem 7.13P
Textbook Problem
305 views

## In a recent statewide election. 55% of the voters rejected a proposal to institute a state lottery. In a random sample of 150 urban precincts, 49% of the voters rejected the proposal. Is the difference significant? Summarize your conclusions in a sentence or two.

Expert Solution
To determine

To find:

The significant difference between the given statements.

### Explanation of Solution

Given:

The given information is,

In a recent statewide election. 55% of the voters rejected a proposal to institute a state lottery. In a random sample of 150 urban precincts, 49% of the voters rejected the proposal.

The five step model for hypothesis testing is:

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For large samples with single sample proportions, the Z value is given by,

Z(obtained)=PsPuPu(1Pu)/N

Where, Ps is the sample proportion,

Pu is the population proportion and,

N is the sample size.

Calculation:

From the given information, the sample size is 150, sample proportion is 49% and the population proportion is 55%.

Follow the steps for two-tailed hypothesis testing as,

Step 1. Making assumptions and meeting test requirements.

Model:

Random sampling.

Level of measurement is interval ratio.

Sampling distribution is Normal.

Step 2. Stating the null hypothesis.

The statement of the null hypothesis is that the proportion of voters from the sample who rejected the proposal are not significantly different from the proportion of voters from the population who rejected the proposal.

Thus, the null and the alternative hypotheses are,

H0:Pu=0.55

H1:Pu0.55

Step 3. Selecting the sampling distribution and establishing the critical region.

Since, the sample is large, Z distribution can be used.

The information given is in the form of proportions, the test for proportion can be used.

Thus, the sampling distribution is Z distribution.

The level of significance is α=0.05.

And area of critical region is Z(critical)=±1

### Want to see the full answer?

Check out a sample textbook solution.See solution

### Want to see this answer and more?

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

See solution

Find more solutions based on key concepts
Show solutions
Other Equations Find all real solutions of the equation. 106. x6 2x3 3 = 0

Precalculus: Mathematics for Calculus (Standalone Book)

Find the limit: limx0x+42x.

Calculus: An Applied Approach (MindTap Course List)

If f(2) = 0, then (2, f(2)) is an inflection point of the curve y = f(x).

Single Variable Calculus: Early Transcendentals, Volume I

State Greens Theorem.

Calculus (MindTap Course List)

In Exercises 39-50, sketch the graph of the function with the given rule. Find the domain and range of the func...

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Subtract: (12)(6)

Elementary Technical Mathematics

For what values of p does the series converge?

Study Guide for Stewart's Multivariable Calculus, 8th

True or False: In the definition of , the expression is interpreted as “the distance between f(x) and L is les...

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user
The text passage describes a statistical hypothesis testing problem where the goal is to determine if there is a significant difference between the proportion of voters who rejected a state lottery proposal in a statewide election (55%) and a random sample of 150 urban precincts (49%).

TYPE: NO_QUESTION

The passage does not contain a direct mathematical question or calculation request. Instead, it provides a context for a statistical hypothesis test and outlines the steps to perform the test. The "question" is implicitly about whether the difference in proportions is statistically significant, but it is not phrased as a direct question. The passage also does not provide a specific answer to this implicit question.