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 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.
c. if appropriate, use the two - proportions $z$-test to conduct the required hypothesis test.
what are the hypotheses for this test?
a $h_0:p_1 = p_2, h_a:p_1>p_2$
b $h_0:p_1 < p_2, h_a:p_1 = p_2$
c $h_0:p_1 = p_2, h_a:p_1 < p_2$
d $h_0:p_1 = p_2, h_a:p_1
eq p_2$
e $h_0:p_1>p_2, h_a:p_1 = p_2$
f $h_0:p_1
eq p_2, h_a:p_1 = p_2$
g using the two - proportions $z$-procedures is not appropriate.
determine the test statistic. if appropriate. select the correct choice below and, if necessary, fill in the answer box to complete your answer
a $z = $ (type an integer or a decimal. round to two decimal places as needed)
b using the two - proportions $z$-procedures is not appropriate.

Explanation:

Step1: Calculate sample proportions

The sample proportion for the first sample is $\hat{p}_1=\frac{x_1}{n_1}=\frac{10}{90}\approx0.111$.
The sample proportion for the second sample is $\hat{p}_2=\frac{x_2}{n_2}=\frac{25}{90}\approx0.278$.
The pooled proportion is $\hat{p}=\frac{x_1 + x_2}{n_1 + n_2}=\frac{10+25}{90+90}=\frac{35}{180}\approx0.194$.

Step2: Calculate the test statistic

The formula for the two - proportions z - test statistic is $z=\frac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1 - \hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}}$.
Substitute the values:

$$
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Answer:

A. $z=-2.83$