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 distribution should be used for a one-sample test for a proportion?
A) t-distribution
B) F-distribution
C) z-distribution
I thought a but was wrong
Z distribution
The correct distribution to be used for a one-sample test for a proportion is the z-distribution.
In this case, you are trying to determine if the proportion of adult women favoring stricter gun laws significantly exceeds 63%. To conduct this test, you need to compare the observed proportion (65.9%) to the hypothesized proportion (63%) and assess if the difference is statistically significant.
For a one-sample test for a proportion, we calculate the test statistic as the difference between the observed proportion and the hypothesized proportion, divided by the standard error of the proportion. The standard error is calculated using the formula:
Standard Error = sqrt(p * (1-p) / n),
where p is the hypothesized proportion and n is the sample size.
Once the test statistic is calculated, we compare it to the critical value obtained from the z-distribution at the desired significance level. If the test statistic is large enough (in absolute value) to fall in the rejection region (typically determined by a two-tailed test), then we reject the null hypothesis and conclude that the proportion is significantly different from the hypothesized value.
Hence, the correct distribution to be used for a one-sample test for a proportion is the z-distribution (Option C).