A bag has 3 red rocks, 4 green rocks, 3 blue rocks, 3 speckled rocks,
and 4 yellow rocks. You randomly pull a rock from the bag, put it
back, and then pull out another one.
What is the probability of getting a green and then a red?

12/17

Step-by-step explanation:

This is an example of probability with replacement

n(red) = 3

n(green) = 4

n(blue) = 3

n(speckled) = 3

n(yellow) = 4

Total = 17

The probability of getting a green = number of green / total number

That is

p(green) = 4/17

Also

p(red) = 3/17

" and " in probability means multiplication , therefore:

the probability of getting a green and then a red will be

4/17 x 3/17 = 12/17

Step-by-step explanation:

Hello!

The study variables are:

: The number of Brand A units sold that required repair.

: THe number of Brand B units sold that required repair.

1. Calculate the difference in the sample proportion for the two brands of computers, p^BrandA−p^BrandB =?.

The sample proportion of each sample is equal to the number of "success" observed xi divided by the sample size n:

^p=

^p=

^p - ^p= 0.1328 - 0.1502= -0.0174

Note: proportions take numbers from 0 to 1, meaning they are always positive. But this time what you have to calculate is a difference between the two proportions so it is absolutely correct to reach a negative number it just means that one sample proportion is greater than the other.

2. What are the correct hypotheses for conducting a hypothesis test to determine whether the proportion of computers needing repairs is different for the two brands?

A. H0:pA−pB=0 , HA:pA−pB<0

B. H0:pA−pB=0 , HA:pA−pB>0

C. H0:pA−pB=0 , HA:pA−pB≠0

If you want to test whether the proportion of computers of both brands is different, you have to do a two-tailed test, the correct option is C.

3. Calculate the pooled estimate of the sample proportion, ^p= ?

To calculate the pooled sample proportion you have to use the following formula:

^p=

4. Is the success-failure condition met for this scenario?

A. Yes

B. No

The conditions that have to be met are:

⇒ Met

⇒ 836 * 0.1328= 111.4192; Met

⇒ 836 * (1 - 0.1328)= 727.5808; Met

⇒ Met

⇒ 739 * 0.1502= 110.9978; Met

⇒  739 * (1-0.1502)= 628.0022; Met

All conditions are met.

5. Calculate the test statistic for this hypothesis test. ? =

6. Calculate the p-value for this hypothesis test, p-value = .

This hypothesis test is two-tailed and so is the p-value, since it has two tails you have to calculate it as:

P(Z≤-0.9902) + P(Z≥0.9902)=  P(Z≤-0.9902) + ( 1 - P(Z≤0.9902))= 0.161 + (1 - 0.839) = 0.322

7. What is your conclusion using α = 0.05?

A. Do not reject H0

B. Reject H0

The decision rule using th ep-value is:

If p-value > α, the decision is to not reject the null hypothesis.

If p-value ≤ α, the decision is to reject the null hypothesis.

The p-value= 0.322 is greater than α = 0.05, so the decision is to not reject the null hypothesis.

8. Compute a 95 % confidence interval for the difference p^BrandA−p^BrandB = ( , )

The formula to calculate the Confidence interval is a little different, because instead of the pooled sample proportion you have to use the sample proportion of each sample to calculate the standard deviation of the distribution:

() ± *

-0.0174 ± 1.965 *

[-0.0520; 0.0172]

I hope it helps!