Based on the Nielsen ratings,the local CBS affiliate claims its 11 p.m. newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers,36% indicated that they watch the late evening news on this local CBS station. What is the critical value if α = 0.01?
A)+2.576
B)+2.326
C)±2.576
D)−2.326

Question

Quizplus · Accepted Answer

To determine the critical value we need to perform a hypothesis test for the proportion.

Null hypothesis: p=0.41
Alternative hypothesis: p<0.41 (since we are looking for the critical value at alpha=0.01)

We can use the normal distribution to find the critical value, since the sample size (100) is large enough to satisfy the conditions of the central limit theorem.

Using a standard normal distribution table, the critical value for a left-tailed test at alpha=0.01 is approximately -2.576.

Therefore, the answer is C (±2.576), since we are looking for the critical value in the left-tail of the distribution.

Based on the Nielsen Ratings,the Local CBS Affiliate Claims Its