# 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
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## 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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