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) Normal model
Is the C? Normal model? I thought it was a t-distribution but got the answer wrong
It is normal model
z-score
No, the correct answer is not C) Normal model. The correct distribution to use for a one-sample test for a proportion is the normal distribution.
When testing the claim about a population proportion, we can approximate the sampling distribution of the sample proportion with a normal distribution under certain conditions. These conditions include a sufficiently large sample size (typically, n * p >= 10 and n * (1 - p) >= 10, where n is the sample size and p is the estimated proportion), as well as independence of observations.
In this case, we are given a sample size of 1026 adults, which is quite large. Therefore, we can use the normal distribution to conduct the hypothesis test.
To test the claim that significantly more than 63% of adult women favor stricter gun laws, we need to set up null and alternative hypotheses and conduct the appropriate statistical test using the normal distribution.