Domestic cats kill many more wild birds in the United States than scientists thought,” states a recent article. Researchers used a sample of n=140 households in the US with cats to estimate that 35% of household cats in the US hunt outdoors.

(a) Find and interpret a 95% confidence interval for the proportion of household cats in the US that hunt outdoors. 

(b) Is it plausible that the proportion of household cats in the US hunting outdoors is 0.45? Is it plausible that it is 0.30?