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StatisticsEssentials Of StatisticsIn 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.BuyFind*arrow_forward*

4th Edition

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Publisher: Cengage Learning,

ISBN: 9781305093836

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.

**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,

Where,

*N* is the sample size.

**Calculation:**

From the given information, the sample size is 150, sample proportion is

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,

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

And area of critical region is

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