According to a Gallup poll conducted in February of 2019, 67% of U.S. adults oppose new construction on border walls. A local newspaper randomly samples 100 adults from its community and finds that 73% oppose further construction on border walls.

What is the probability that a randomly selected sample of 100 U.S. adults will have an error of more than 5% either above or below the population proportion?

The following questions break down the steps to finding this probability.

Multiple choice

1. The first step is to check normality conditions. We check normality conditions to verify thatis [Blank] normal in shape. A. the distribution of sample proportions

B. distribution of z-scores

C. distribution in the opinions in the population

1B. For this problem, the expected count of successes np is [ Select ] 67, 73, 33, 27 ; this is the number we expect to oppose wall construction in the sample of 100.

The expected count of failures n(1-p) is [ Select ] 33, 27, 67, 73 ; this is the number we expect to support wall construction in the sample of 100.

When both the expected counts are at least [ Select ] 10, 100, depends on the problem , we can use a normal model to estimate probabilities.

2. Next step is to use the Normal Distribution Calculator to find the area that represents the appropriate probability. We are trying to estimate the probability that the error in the random sample is more than 0.05.

We use the Z-score we calculated previously. Because of the symmetry in the normal curve, we can use Z = +1.06 or Z = -1.06. We arbitrarily chose Z=+1.06.

What is the probability that the error in the random sample is more than 0.05?

• about 29%
• about 14%
• about 71%
• about 86%

3. In the 2008 presidential election newspapers reported that Obama received 40% of the white male vote. If this is true, what is the probability that a random sample of 1,000 white male voters estimates this percentage within 3% error?

• about 2 to 3%
• about 4 to 6%
• about 95 to 96%
• We cannot determine the probability because a normal model is not a good fit for the sampling distribution.

4. According to a Yale University poll conducted in December 2018, 70% of U.S. adults think that global warming is happening. If this is true, what is the probability that a random sample of 525 U.S. adults will estimate this parameter within 3 percentage points?

• about 87%
• about 93%
• about 13%
• It is impossible to tell because normality conditions are not met