A new study shows that relationship status on Facebook matters to couples. The study included 58 college-age heterosexual couples who had been in a relationship for an average of 19 months. In 45 of the 58 couples, both partners reported being in a relationship on Facebook. In 31 of the 58 couples, both partners showed their dating partner in their Facebook profile picture. Men were somewhat more likely to include their partner in the picture than vice versa. However, the study states: ‘‘Females’ indication that they are in a relationship was not as important to their male partners compared with how females felt about male partners indicating they are in a relationship.” Using a population of college-age heterosexual couples who have been in a relationship for an average of 19 months:

(a) A 95% confidence interval for the proportion with both partners reporting being in a relationship on Facebook is about 0.66 to 0.88. What is the conclusion in a hypothesis test to see if the proportion is different from 0.5? What significance level is being used?

(b) A 95% confidence interval for the proportion with both partners showing their dating partner in their Facebook profile picture is about 0.40 to 0.66. What is the conclusion in a hypothesis test to see if the proportion is different from 0.5? What significance level is being used?