Question

the numbers of successes and the sample sizes for independent simple random samples from two populations are provided for a left - tailed test and an 80% confidence interval. complete parts (a) through (d)
$x_1 = 10,n_1 = 90,x_2 = 25,n_2 = 90,\alpha=0.10$
click here to view a table of areas under the standard normal curve for negative values of z.
click here to view a table of areas under the standard normal curve for positive values of z.

determine the sample proportions.
determine the sample proportion $\hat{p}_1$
$\hat{p}_1 = 0.111$ (type an integer or a decimal. round to three decimal places as needed.)
determine the sample proportion $\hat{p}_2$
$\hat{p}_2=\square$ (type an integer or a decimal. round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for sample proportion

The formula for sample proportion is $\hat{p}=\frac{x}{n}$, where $x$ is the number of successes and $n$ is the sample size.

Step2: Calculate $\hat{p}_{2}$

Given $x_{2} = 25$ and $n_{2}=90$. Substitute into the formula: $\hat{p}_{2}=\frac{25}{90}$.
Simplify the fraction: $\frac{25}{90}=\frac{5}{18}\approx0.278$.

Answer:

$\hat{p}_{2} = 0.278$