A USU Today survey found that of the gun owners surveyed 55% favor stricter gun laws. The survey

Involved 500 gun owners. Test the claim that a majority (more than 50%) of gun owners favor stricter gun laws. Use a .05 significance level.

To test the claim that a majority of gun owners favor stricter gun laws, we need to perform a hypothesis test. Here are the steps to carry out the test:

Step 1: Set up the hypotheses.
- Null hypothesis (H0): p = 0.50 (proportion of gun owners favoring stricter gun laws is 50%)
- Alternative hypothesis (HA): p > 0.50 (proportion of gun owners favoring stricter gun laws is greater than 50%)

Step 2: Select a significance level.
The question states to use a 0.05 significance level, which correspondingly means the critical region will be in the right tail of the distribution.

Step 3: Collect and summarize the data.
According to the survey, among the 500 gun owners surveyed, 55% favor stricter gun laws. This means there were 0.55 * 500 = 275 gun owners who favor stricter gun laws.

Step 4: Calculate the test statistic.
The test statistic for testing a proportion can be calculated using the formula:
Z = (p̂ - p) / √(p * (1-p) / n)
where p̂ is the sample proportion, p is the null hypothesis proportion, and n is the sample size.

Using the given information, we have:
p̂ = 0.55
p = 0.50
n = 500
Plugging these values into the formula, we get:
Z = (0.55 - 0.50) / √(0.50 * (1-0.50) / 500)

Step 5: Determine the critical value and make a decision.
At a significance level of 0.05, the critical value for a right-tailed test is 1.645.

If the calculated Z value is greater than 1.645, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

Step 6: Calculate the p-value and make a decision.
If the p-value is less than the significance level (0.05), we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

To calculate the p-value, we use the standard normal distribution table or a calculator to find the probability of obtaining a Z value greater than the calculated one.

Step 7: State the conclusion.
Based on the test statistic or p-value, we can state our conclusion about the claim.

Now, you just need to plug the given values into the formula in Step 4 and calculate the Z value. Then compare it with 1.645 to make a decision or calculate the p-value to determine the conclusion.

Using a formula for a binomial proportion one-sample z-test with your data included, we have:

z = .55 - .50 / √[(.50)(.50)/500]
Finish the calculation.

Use a z-table to find the critical or cutoff value at 0.05 for a one-tailed test.

If the z-test statistic calculated above exceeds the critical value from the z-table, reject the null. If the z-test statistic does not exceed the critical value from the z-table, do not reject the null.

I hope this will help get you started.

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