Question

If n=590 and p=0.93, construct a 90\% confidence interval.

Confidence intervals
If $$\displaystyle{n}={590}$$ and $$\displaystyle{p}={0.93}$$, construct a $$\displaystyle{90}\%$$ confidence interval.

2021-08-03
Step 1
Express the expression for the confidence interval.
$$\displaystyle{C}.{I}={p}\pm{Z}\cdot\sqrt{{{\frac{{{p}{\left({1}-{p}\right)}}}{{{n}}}}}}$$
Here, Z* is the critical value .
From the Z table, the value corresponding to the region 90.5 is,
$$\displaystyle{Z}\cdot={1.31}$$
Step 2
Put 590 for n, 0.93 for p, 1.31 for Z* implies,
$$\displaystyle{C}.{I}={0.93}\pm{1.31}\sqrt{{{\frac{{{0.93}{\left({1}-{0.93}\right)}}}{{{0.93}}}}}}$$
$$\displaystyle{C}.{I}={0.93}\pm{0.346}$$
Thus, the confidence interval is $$\displaystyle{0.93}+{0.346}$$ and $$\displaystyle{0.93}-{0.346}$$.