Question

3. An IAB study on the state of original digital video showed that original digital video is becoming increasingly popular. Original digital video is defined as professionally produced video intended only for ad-supported online distribution and viewing. According to IAB data, 30% of American adults 18 or older watch original digital videos each month.
a. Suppose that you take a sample of 100 US adults. If the population proportion of US adults who watch original digital videos is 0.30, what is the probability that fewer than 25% in your sample will watch original digital videos?
b. Suppose that you take a sample of 500 US adults. If the population proportion of US adults who watch original video is 0.30, what is the probability that fewer than 25% in your sample will watch original digital videos?
c. Discuss the effect of sample size on the sampling distribution of proportion in general and the effect on the probabilities in (a) and (b).

Answer 1

Answer: Given, that there are 30% of American adults 18 or older watch original a) digital videos eacn month. Therefore, the population proportion is 0.30 The probability that the sample proportion is fewer than 25% when the sample size is 100: 0.25 - A р-л P(p< 0.25) = P 7(1-7) 7(1-7) 0.25 – 0.30 = P Z<. 0.30(1-0.30) 100 = P(Z<-1.091) = 0.1376

b) the probability that the sample proportion is fewer than 25% when the sample size is 500 is: 0.25 - A р- п P(p<0.25) = P 7(1-7) 7(1-7) п 0.25 – 0.30 = P Z<- 0.30(1-0.30) 500 = P(Z <-2.44) %3D = 0.0073

The sample size increases the standard error will decreases and then automatically the distribution curve will narrow for the sampling distribution of proportions. That is, the probability of true proportion of fewer than 25% part (b) is smaller than the probability of fewer than 25% in part (a).