Math / Data & Statistics

QuestionEvaluate $z=\frac{\hat{p}_{1}-\hat{p}_{2}-0}{S E}$ for $\hat{p}_{1}=0.413, \hat{p}_{2}=0.343$ , and $S E=0.165$ $z=$ $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

What is this asking? We're simply plugging numbers into a formula and calculating the result!
Specifically, we're finding a value called $z$ by substituting given values for $\hat{p}_{1}$ , $\hat{p}_{2}$ , and $SE$ . Watch out! Be careful with the order of operations, especially the subtraction in the numerator.
Also, remember to round the final answer to two decimal places.

STEP 2

1. Substitute the values
2. Calculate the numerator
3. Calculate the final result

STEP 3

Alright, let's kick things off by plugging in the given values into our formula for $z$ .
We have $\hat{p}_{1} = \textbf{0.413}$ , $\hat{p}_{2} = \textbf{0.343}$ , and $SE = \textbf{0.165}$ .
So, our formula becomes: $z = \frac{0.413 - 0.343 - 0}{0.165}$

STEP 4

Now, let's tackle the numerator.
We have $0.413 - 0.343 - 0$ .
Remember, subtracting zero doesn't change a number!
So, we just need to calculate $0.413 - 0.343$ . $0.413 - 0.343 = \textbf{0.07}$ So, our numerator is 0.07.

STEP 5

With our numerator simplified, our equation looks like this: $z = \frac{0.07}{0.165}$ Now, we just need to perform the division to find our final result: $z = \frac{0.07}{0.165} \approx \textbf{0.4242424...}$

STEP 6

Almost there!
The problem asks us to round to two decimal places.
Looking at our result, the third decimal place is 4, which is less than 5, so we round down.
Our final answer, rounded to two decimal places, is $\textbf{0.42}$ .

STEP 7

Therefore, $z \approx 0.42$ .

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QuestionEvaluate $z=\frac{\hat{p}_{1}-\hat{p}_{2}-0}{S E}$ for $\hat{p}_{1}=0.413, \hat{p}_{2}=0.343$ , and $S E=0.165$ $z=$ $\square$ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

STEP 2

1. Substitute the values
2. Calculate the numerator
3. Calculate the final result

STEP 3

Alright, let's kick things off by plugging in the given values into our formula for $z$ .
We have $\hat{p}_{1} = \textbf{0.413}$ , $\hat{p}_{2} = \textbf{0.343}$ , and $SE = \textbf{0.165}$ .
So, our formula becomes: $z = \frac{0.413 - 0.343 - 0}{0.165}$

STEP 4

Now, let's tackle the numerator.
We have $0.413 - 0.343 - 0$ .
Remember, subtracting zero doesn't change a number!
So, we just need to calculate $0.413 - 0.343$ . $0.413 - 0.343 = \textbf{0.07}$ So, our numerator is 0.07.

STEP 5

With our numerator simplified, our equation looks like this: $z = \frac{0.07}{0.165}$ Now, we just need to perform the division to find our final result: $z = \frac{0.07}{0.165} \approx \textbf{0.4242424...}$

STEP 6

Almost there!
The problem asks us to round to two decimal places.
Looking at our result, the third decimal place is 4, which is less than 5, so we round down.
Our final answer, rounded to two decimal places, is $\textbf{0.42}$ .

STEP 7

Therefore, $z \approx 0.42$ .

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QuestionEvaluate z=p^1−p^2−0SEz=\frac{\hat{p}_{1}-\hat{p}_{2}-0}{S E}z=SEp^​1​−p^​2​−0​ for p^1=0.413,p^2=0.343\hat{p}_{1}=0.413, \hat{p}_{2}=0.343p^​1​=0.413,p^​2​=0.343, and SE=0.165S E=0.165SE=0.165 z=z=z= □\square□ (Round to two decimal places as needed.)

Studdy Solution

STEP 1

STEP 2

1. Substitute the values2. Calculate the numerator3. Calculate the final result

STEP 3

STEP 4

STEP 5

STEP 6

Almost there!The problem asks us to **round to two decimal places**.Looking at our result, the third decimal place is 4, which is less than 5, so we round down.Our **final answer**, rounded to two decimal places, is 0.42\textbf{0.42}0.42.

STEP 7

Therefore, z≈0.42z \approx 0.42z≈0.42.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionEvaluate $z=\frac{\hat{p}_{1}-\hat{p}_{2}-0}{S E}$ for $\hat{p}_{1}=0.413, \hat{p}_{2}=0.343$ , and $S E=0.165$ $z=$ $\square$ (Round to two decimal places as needed.)

1. Substitute the values
2. Calculate the numerator
3. Calculate the final result

Almost there!
The problem asks us to round to two decimal places.
Looking at our result, the third decimal place is 4, which is less than 5, so we round down.
Our final answer, rounded to two decimal places, is $\textbf{0.42}$ .

Therefore, $z \approx 0.42$ .