To compare the popularity rates of two different political candidates in their respective states, a random sample of 212 citizens from state a yielded 145 who were in favor of their state's candidate whereas 128 citizens out of the 200 selected from state b were in favor of their state's candidate. we wish to use a significance level of 0.05 to test whether there exists a difference between the popularity rates of these two candidates.

There exists no difference between the popularity rates of these two candidates.

Step-by-step explanation:

Given : a random sample of 212 citizens from State A yielded 145 who were in favor of their state's candidate whereas 128 citizens out of the 200 selected from State B were in favor of their state's candidate.

To Find :  We wish to use a significance level of 0.05 to test whether there exists a difference between the popularity rates of these two candidates.

Solution:

A random sample of 212 citizens from State A yielded 145 who were in favor of their state's candidate

So,

128 citizens out of the 200 selected from State B were in favor of their state's candidate.

We will use Comparing Two Proportions

Let p_1 and p_2 be the probabilities of the popularity rates of these two candidates.

Formula of test statistic :

Substitute the values  

 test statistic :

 test statistic : 0.856

refer z table for p value

p value = 0.8023

α = 0.05

Since p value >α

So, we accept the null hypothesis

Hence there exists no difference between the popularity rates of these two candidates.

the ratio of grapes to blueberries she should use is 12: 3

step-by-step explanation:

if mandie is making 15 cups of fruit salad, the ratio of grapes to blueberries she should use is 12: 3.