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.
See previous post.
To test the claim that a majority of gun owners favor stricter gun laws, we can use a hypothesis test. Here's how you can conduct the test:
Step 1: Set up the hypotheses.
- Null hypothesis (H0): The proportion of gun owners favoring stricter gun laws is equal to or less than 50%. (p ≤ 0.50)
- Alternative hypothesis (Ha): The proportion of gun owners favoring stricter gun laws is greater than 50%. (p > 0.50)
Step 2: Determine the significance level.
In this case, the significance level (α) is given as 0.05.
Step 3: Calculate the test statistic.
To calculate the test statistic, we can use the formula for a test of proportions:
z = (p̂ - p) / √(p(1-p) / n)
Where:
- p̂ is the sample proportion (55% or 0.55)
- p is the hypothesized proportion (50% or 0.50)
- n is the sample size (500)
Calculating the test statistic:
z = (0.55 - 0.50) / √(0.50 * (1 - 0.50) / 500)
Step 4: Find the critical value.
Since the alternative hypothesis is that the proportion is greater than 50%, we'll be testing in the right tail of the normal distribution. As the significance level is 0.05 (5%), the critical value can be found using a z-table or a statistical software. For the significance level of 0.05, the critical value is approximately 1.645.
Step 5: Make the decision.
Compare the test statistic to the critical value. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Step 6: Interpret the decision.
If we reject the null hypothesis (H0), we can conclude that there is evidence to suggest that a majority of gun owners favor stricter gun laws. If we fail to reject the null hypothesis, we do not have enough evidence to conclude that a majority of gun owners favor stricter gun laws.
Note: It's important to mention that this calculation assumes the survey is representative of all gun owners, and the sample was selected randomly.