A spokesperson from the National Rifle Association (NRA) states that 45% of the households in the United States contain at least one firearm. Assume that this is your population value. Your goal was to take a random sample of 200 homes, but your research yielded only 29 responses. And you find out that only about 23% of them contain a firearm. You want to test the null hypothesis that the population proportion is 45% against the alternative that it is less than that. You set your alpha at .01. Required:
With n=29, you will use the t-statistic and the sampling distribution of the t to perform the hypothesis test.