Question

23. A poll of 250 people shows the supporting rates of two candidates of the state congress: - candidate A: 28.3%±3%; candidate B: 32.1%±3%. Do we conclude that candidate B’s supporting rate is higher than candidate A (or can we reject the hypothesis that the two candidates’ supporting rates are same)? Why? What if the supporting rates of a poll are 28.5%±2% for A and 32.7%±2% for B? Why?

Answer 1

a)

A - 28.3 % +- 3 %

= (25.3% , 31.3%)

B = (32.1% +- 3 %)

=(29.1 % , 35.1%)

since lower bound of B = 29.1% is less than upper bound of A (31.3 %)

we can't say B’s supporting rate is higher than candidate A

b)

similarly

A = (26.5 % , 30.5%)

B = (30.7% , 34.7)%

yes, we can conclude that candidate B’s supporting rate is higher than candidate A

lower bound of B = 30.7% is greater than upper bound of A (30.5 %)