Question

TV advertising agencies face growing challenges in reaching audience members because viewing TV programs via digital streaming is increasingly popular. The Harris poll reported on November 13, 2012 that 53% of 2343 American adults surveyed said they have watched digitally streamed TV programming on some type of device. Someone claimed that fewer than 50% of American adults watch digitally streamed TV programming.

a) What is the distribution of the sample proportion for this scenario? Justify your answer.

b) Use an appropriate statistic to test at α = 0.05 the claim that fewer than 50% of American adults watch digitally streamed TV.

Write the null and alternative hypotheses, write down the assumptions, calculate the value of the test statistic, determine the p-value,

state your conclusion in the context of the original question.

Answer 1

Let p denotes the true proportion of American adults watch digitally streamed TV programming.

a) Here,

, so we can approximate the sampling distribution of sample mean by normal distribution.

b)

There is not sufficient evidence to support the claim that fewer than 50% of American adults watch digitally streamed TV programming.