To determine the sample size and the 95% confidence interval for the proportion of respondents who "strongly agree" that K-12 schools should teach critical thinking to children, follow these steps:
1. Identify the sample size.
- The poll was conducted with a sample size of 1001 Americans age 18 and over.
Therefore, the sample size is 1001.
2. Look at the given proportion and margin of error.
- The proportion of respondents who "strongly agree" is 80%, or 0.80 when expressed as a decimal.
- The margin of error for this survey is 3.2%, or 0.032 when expressed as a decimal.
3. Calculate the lower and upper bounds of the confidence interval.
- The lower bound is calculated by subtracting the margin of error from the proportion:
[tex]\[
\text{Lower Bound} = 0.80 - 0.032 = 0.768
\][/tex]
- The upper bound is calculated by adding the margin of error to the proportion:
[tex]\[
\text{Upper Bound} = 0.80 + 0.032 = 0.832
\][/tex]
4. Convert these bounds to percentages and round to one decimal place:
- Lower Bound as a percentage:
[tex]\[
0.768 \times 100 = 76.8\%
\][/tex]
- Upper Bound as a percentage:
[tex]\[
0.832 \times 100 = 83.2\%
\][/tex]
So the 95% confidence interval is from 76.8% to 83.2%.
Therefore, the results summarize as follows:
- Sample size: 1001
- 95% Confidence Interval: 76.8% to 83.2%
