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
a. 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 $\hat{p}_2$
$\hat{p}_2 = 0.278$ (type an integer or a decimal. round to three decimal places as needed)
determine the pooled sample proportion $\hat{p}_p$
$\hat{p}_p = 0.194$ (type an integer or a decimal. round to three decimal places as needed)
b. decide whether using the two - proportions z - procedures is appropriate.
check that the assumptions are satisfied. select all that apply.
a. the assumptions are satisfied, so using the procedures is appropriate
b. since $n_2 - x_2$ is less than 5, using the procedures is not appropriate
c. since $x_2$ is less than 5, using the procedures is not appropriate.
d. since $x_1$ is less than 5, using the procedures is not appropriate.
e. since $n_1 - x_1$ is less than 5, using the procedures is not appropriate.

Explanation:

Step1: Check conditions for first sample

For the first sample, \(n_1 = 90\), \(x_1=10\). Then \(n_1 - x_1=90 - 10 = 80\). Since \(x_1 = 10\geq5\) and \(n_1 - x_1=80\geq5\).

Step2: Check conditions for second sample

For the second sample, \(n_2 = 90\), \(x_2 = 25\). Then \(n_2 - x_2=90 - 25=65\). Since \(x_2 = 25\geq5\) and \(n_2 - x_2 = 65\geq5\).

Answer:

A. The assumptions are satisfied, so using the procedures is appropriate.