Question

A recent survey of 128 high school students indicated the following information about release times from school. -35 percent wanted to start school and hour earlier and get out earlier -20 percent liked things how there are currently -39 percent wanted to start school a half an hour later and get out later in the day. -6 percent had no opinion The margin of error for this survey was calculated to be plus or minus 4 percent. The sample size n=128 Find the interval estimates for those that want to get out earlier and those that want to get out later. Explain how it would be possible for the group that wants to get out of school earlier to win after all the votes are counted.

Answer 1

Answer:

The interval is for those that want to get out earlier is between 43 student to 47 students

The interval is for those that want to get out later is between 48 student to 50 students

Step-by-step explanation:

Given that:

sample size n=128

Probability of those  that want to get out earlier = 0.35.

The mean  =  n × probability = 0.35 × 128 = 44.8 ≈ 45

Margin of error = 4% = 0.04 × 44.8 = 1.79 ≈ 2

Therefore the interval = mean ± Margin of error = 45 ± 2 = (43, 47)

The interval is for those that want to get out earlier is between 43 student to 47 students

Probability of those  that want to get out later = 0.39.

The mean  =  n × probability = 0.39 × 128 = 49.92 ≈ 50

Margin of error = 4% = 0.04 × 50 =  2

Therefore the interval = mean ± Margin of error = 50 ± 2 = (48, 52)

The interval is for those that want to get out later is between 48 student to 50 students

the group that wants to get out of school earlier to win after all the votes are counted if those that have no opinion decide that they want to go earlier