Question

Gavin was playing with a spinner that has 4 equal areas, numbered 1, 2, 3, and 4.

Gavin spun the spinner 100 times, and 26 of the 100 spins came up as a 4. He wanted to see how likely a result of 26 fours in 100 spins would be with a fair spinner, so Gavin used a computer simulation to see the proportion of fours in 100 spins, repeated 100 times, assuming a probability of spinning a 4. Create a 95% confidence interval based on the data from the simulation, to the nearest hundredth, and state whether the observed proportion of fours is within the margin of error of the simulation results.

A) 95% Confidence Interval: [X, Y]
B) Is the observed proportion of fours within the margin of error?
a) Yes
b) No

Answer 1

To create a 95% confidence interval for the proportion of fours in 100 spins, use the plus-four method. The observed proportion of fours is within the margin of error of the simulation results.

Step-by-step explanation:

To create a 95% confidence interval for the proportion of fours in 100 spins, we can use the plus-four method.

The observed proportion of fours is 26/100 = 0.26. To adjust for the error in calculating the confidence interval, we add 2 successes and 2 failures, resulting in a new sample size of 100 + 4 = 104 spins.

Using the plus-four method, the confidence interval can be calculated as follows:

Lower bound = (26 + 2) / (100 + 4) = 0.28

Upper bound = (26 + 2) / (100 + 4) = 0.32

Therefore, the 95% confidence interval for the proportion of fours in 100 spins is [0.28, 0.32].

The observed proportion of fours (0.26) is within the margin of error of the simulation results because it falls within the confidence interval.