In a recent Gallup poll randomly selected adults in the Unit

In a recent Gallup poll, randomly selected adults in the United States were asked if they have a gun in their home, and 37.2% of them answered \"yes\" based on a hypothesis test, can we safely conclude that less than 50% of adults answer \"yes\" when asked if they have a gun in their home.

Solution

proportion of adults who answered yes = p = 0.372.....
Test H0 : Population proportion < = 0.50 against population proportion > 0.50.....

test statistic = ( 0.372 - 0.50) / sqrt [ 0.5 * 0.5 /100 ] = -2.56.....
p-value = 0.005233608
which is less than any standard level of significance say, 0.01!
so, we have to reject H0 and we cannot safely conclude that less than 50% of adults answer \"yes\" when asked if they have a gun in their home.