A usu today survey foudn that of the gun owners surveyed 275 favor sticter gun laws. The survey involved 500 gun owners. Test the claim that a mojority( more than 50%) of gun owners favor stricter fun laws. use .05 significane level

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

z = .55 - .50 / √[(.50)(.50)/500] -->note: .55 is 275/500 in decimal form.
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.

To test the claim that a majority of gun owners favor stricter gun laws, we can use a hypothesis test. The null hypothesis (H₀) assumes that the true proportion of gun owners favoring stricter gun laws is equal to or less than 50%, while the alternative hypothesis (H₁) assumes that the true proportion is greater than 50%.

Let's go through the steps to conduct the hypothesis test:

Step 1: Define the hypotheses:
H₀: p ≤ 0.5
H₁: p > 0.5

Where 'p' represents the proportion of gun owners who favor stricter gun laws.

Step 2: Set the significance level (α):
The significance level, denoted as α, determines the probability of rejecting the null hypothesis when it is true. In this case, the significance level is given as 0.05 (or 5%).

Step 3: Calculate the test statistic:
To calculate the test statistic, we need to find the standard error of the proportion and the observed statistic.

The standard error of the proportion (SE) can be calculated using the following formula:
SE = sqrt[(p * (1 - p)) / n]

Where 'p' is the proportion of gun owners favoring stricter gun laws (275/500 = 0.55), and 'n' is the sample size (500 in this case).

Next, we can calculate the observed statistic, which is the z-score, using the formula:
z = (p - P₀) / SE

Where P₀ is the hypothesized proportion under the null hypothesis, which is 0.5 in this case.

Step 4: Determine the critical value:
Since the alternative hypothesis is one-tailed (greater than), we need to find the critical value using the significance level and the z-table. A z-value that corresponds to a 5% significance level is approximately 1.645.

Step 5: Compare the test statistic with the critical value:
If the test statistic (z) is greater than the critical value, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.

Let's calculate the test statistic and make the comparison:

SE = sqrt[(0.55 * (1 - 0.55)) / 500] ≈ 0.022009
z = (0.55 - 0.5) / 0.022009 ≈ 2.267

The calculated z-value is approximately 2.267, which is greater than the critical value of 1.645 at a 5% significance level.

Step 6: Make a conclusion:
Since the calculated z-value is greater than the critical value, we reject the null hypothesis. This means we have enough evidence to support the claim that a majority of gun owners favor stricter gun laws at a 5% significance level.

In summary, based on the survey results and conducting a hypothesis test, it can be concluded that there is evidence to suggest that a majority of gun owners favor stricter gun laws.