In a study of 2302 U.S. adults surveyed online by Harris Interactive 1243 respondents indicated that they tend to not trust the press. Using an a = 0.05 level of significance, does this indicate that more than half of U.S. adults tend to not trust the press?
The only requirement for the sign test is that our sample be obtained randomly. When dealing with nominal data, we can identify a characteristic of interest and then determine whether each individual in the sample possesses this characteristic. Under the null hypothesis in the sign test, we expect that half of the data will result in minus signs and half in plus signs. If we let a plus sign indicate the presence of the characteristic (and a minus sign indicate the absence), we expect half of our sample to possess the characteristic while the other half will not. Letting p represent the proportion of the population that possesses the characteristic, our null hypothesis will be H0: p = 0.5. Use the sign test for Problems 17 and 18, following the sign convention indicated previously.