A USU today survey found that of the gun owners surveyed 275 favor stricter gun laws. Test the claim that the majority (more than 50%) of gun owners favor stricter gun laws. Use a .05 significance level.
How many gun owners were surveyed?
To test the claim that the majority of gun owners favor stricter gun laws, we can use a hypothesis test. Here's how you can perform the test:
Step 1: State the hypotheses:
The null hypothesis (H0): The proportion of gun owners favoring stricter gun laws is equal to or less than 50%.
The alternative hypothesis (Ha): The proportion of gun owners favoring stricter gun laws is greater than 50%.
Step 2: Set the significance level:
In this case, the significance level is given as 0.05, which means we want to be 95% confident in our results.
Step 3: Collect and summarize the data:
The survey found that out of the gun owners surveyed, 275 favor stricter gun laws. However, we also need the total number of gun owners surveyed to calculate proportions.
Step 4: Perform the hypothesis test:
We can use a one-sample proportion test to compare the observed proportion in the sample (275 gun owners favoring stricter gun laws) to the expected proportion under the null hypothesis (50%).
Step 5: Calculate the test statistic and p-value:
Using the sample proportion, expected proportion, and the sample size, we can calculate the test statistic (Z-score) and the corresponding p-value.
Step 6: Draw a conclusion:
If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence to support the claim that the majority of gun owners favor stricter gun laws. Otherwise, if the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis and do not have sufficient evidence to support the claim.
Note: Since we don't have the actual total number of gun owners surveyed, it is not possible to complete the hypothesis test calculation. However, I have outlined the steps you would follow if you had all the necessary data.