Politicians are interested in knowing the opinions of their constituents on important issues. One administrative assistant to a senator claims that more than 63% of adult women favor stricter gun laws. A recent telephone survey of 1026 adults by IBR Polls found that 65.9% of adult women favored stricter gun laws. Test the claim that significantly more than 63% of adult women favor stricter gun laws.
What is the p-value? Enter the answer rounded to three (3) decimal places.
You can try a proportional one-sample z-test for this one since this problem is using proportions.
Null hypothesis:
Ho: p = .63 -->meaning: population proportion is equal to .63
Alternative hypothesis:
Ha: p > .63 -->meaning: population proportion is greater than .63 (this is a one-tailed test)
Using a formula for a proportional one-sample z-test with your data included, we have:
z = (.659 - .63)/√[(.63)(.37)/1026] --> .37 represents 1-.63 and 1026 is sample size.
Finish the calculation. To find the p-value for the test statistic, check a z-table. The p-value is the actual level of the test statistic.
Is it 3.165?
To test the claim, we can use a hypothesis test.
The null hypothesis (H0) is that the proportion of adult women who favor stricter gun laws is 63% or less. The alternative hypothesis (Ha) is that the proportion is more than 63%.
To find the p-value, we can use the Z-test for proportions.
1. Calculate the test statistic (Z-score):
Z = (p - p0) / sqrt(p0 * (1 - p0) / n)
Where:
- p is the sample proportion (65.9% = 0.659)
- p0 is the hypothesized proportion (63% = 0.63)
- n is the sample size (1026)
Plugging in the values:
Z = (0.659 - 0.63) / sqrt(0.63 * (1 - 0.63) / 1026)
= 1.4794
2. Find the p-value:
The p-value corresponds to the area under the normal curve to the right of the test statistic (Z = 1.4794).
Using a standard normal distribution table or a calculator, we find that the p-value is approximately 0.070.
Therefore, the p-value is 0.070 (rounded to three decimal places).
Next, we need to interpret the p-value:
- If the p-value is less than the significance level (often denoted as α), we reject the null hypothesis.
- If the p-value is greater than or equal to the significance level, we fail to reject the null hypothesis.
Since the p-value (0.070) is greater than the standard significance level of 0.05, we fail to reject the null hypothesis. This means that there is not enough evidence to support the claim that significantly more than 63% of adult women favor stricter gun laws based on the sample data.