Question

Senator Lott claims that 50% of Americans want federal funding for PBS cut. You, a devout fan of “Barney” and “Lamb Chop” (sadly, Shari Lewis passed away in 1998), are deeply suspicious of this claim. So, you decide to take your own unbiased poll.  You sample 250 people and find that 46% want to see the cuts in funding. Perform a hypothesis test, and give your conclusions. (The question below was an issue a few years ago when Trent Lott was in the Senate)

1. State your Null Hypothesis – use words, not just a percentage.

2. Find the standard deviation using claim percentage as p and the survey size as n.

3. What is the observed percentage? Enter your answer.

4. Compare your observed percentage to the interval of p± 2?. Construct the proper sentence either rejecting or not rejecting the null hypothesis.

5. Write your conclusion in your words.

Answer 1

Solution:

a. Null Hypothesis (Ho): p = 0.50, the population proportion of Americans want federal funding for PBS cut is 50%.

Alternative Hypothesis (Ha): p 0.50, the population proportion of Americans want federal funding for PBS cut is not 50%.

b. Standard deviation, = np (1 - p) = 250*0.5*0.5 = 7.906

c. Test Statistics

Z = (0.46 - 0.50)/0.50 (1-0.50)/250

Z = -0.04/0.03162

Z = -1.26

d. Since test statistics lie within 2 standard deviation from the population proportion, therefore we fail to reject the null hypothesis.

e. Hence, we can conclude that the population proportion of Americans want federal funding for PBS cut is 50%.