Out of a 54 person sample from our fall Math-150 classes, 12.4\% of the students are left-handed. Use a TI 84 graphing calculator to construct an 80\% confidence interval for the population proportion.

Out of a 54 person sample from our fall Math-150 classes, $$\displaystyle{12.4}\%$$ of the students are left-handed. Using a TI 84 graphing calculator:
Construct an $$\displaystyle{80}\%$$ confidence interval for the population proportion, p. Round to tenths of a percent and write a sentence answer.
The U.S. has $$\displaystyle{13.1}\%$$ of it’s population that are left-handed. Did this fall in your confidence interval from part a?
Be sure to show all calculator commans used.

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Step 1
Given information:
$$\displaystyle{n}={54}$$
$$\displaystyle\hat{{{p}}}={0.124}$$
$$\displaystyle{x}={54}\times{0.124}$$
Confidence level $$\displaystyle={80}\%$$
Step 2
The step by step procedure to determine confidence interval for proportion:
1) Press STAT and scroll right to the TESTS menu.
2) Scroll down to A:1-PropZInt and press ENTER.
3) Enter the values, $$\displaystyle{x}={6.696},\ {n}={54}$$ and C-Level $$\displaystyle={0.80}.$$
4) Select Calculate and press ENTER. NKS Step 3
The obtained $$\displaystyle{80}\%$$ confidence interval for the population proportion, p is $$\displaystyle{\left({0.0665},\ {0.1815}\right)}$$.
Yes the proportion of left handed in U.S i.e $$\displaystyle{13.1}\%$$ falls in our confidence interval $$\displaystyle{\left({0.0665},\ {0.1815}\right)}$$.