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.

UkusakazaL 2021-08-06 Answered
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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Expert Answer

Elleanor Mckenzie
Answered 2021-08-10 Author has 14316 answers
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 \(\displaystyle{\left({0.0665},\ {0.1815}\right)}\).
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