The following portion of a flow diagram shows that the expression ab + cd is equivalent to the expression dc + ba.

fill in each circle with the appropriate symbol: either c+ (for the commutative property of addition) or cx (for the commutative property of multiplication).

a. ax, cx, a+

b. ax, ax, a+

c. cx, cx, c+

d. c+, c+, cx

Do social recommendations increase ad effectiveness? a study of online video viewers compared viewers who arrived at an advertising video for a particular brand by following a social media recommendation link to viewers who arrived at the same video by web browsing. data were collected on whether the viewer could correctly recall the brand being advertised after seeing the video. the results are given below. correctly recalled the brandarrival 409153browsing20484b. conduct the hypothesis test, using the 0.025 level of significance. what is the value of the test statistic? χ2stat=what is the p-value? p-value=is this value significant atα=0.025?

1. if events a and b are non-overlapping events, how do you find the probability that one or the other occurs? 2. what does it mean if p(a or b) equals 1?

Unaware that 35% of the 10000 voters in his constituency support him, a politician decides to estimate his political strength. a sample of 200 voters shows that 40% support him. a. what is the population? b. what is the parameter of interest? state its value c. what is the statistics of the interest? state its value d. compare your answers in (b) and (c) is it surprising they are different? if the politician were to sample another 200 voters, which of the two numbers would most likely change? explain