Math / Data & Statistics

QuestionFor the following claim, state the null and alternative hypothesis. A research study concludes that the high school graduation rate in the United States is higher than the high school graduation rate in Europe, Let $p_{1}$ represent the high school graduation rate in the United States.
The null hypothesis is $H_{0}$ : $\square$ .
The alternative hypothesis is $H_{1}$ : $\square$ .
$p_{1}$ $p_{2}$

Studdy Solution

STEP 1

What is this asking? We need to figure out how to write the null and alternative hypotheses for comparing high school graduation rates in the US and Europe. Watch out! Don't mix up the null and alternative hypotheses!
The null hypothesis is what we're trying to disprove, and the alternative is what we suspect is true.

STEP 2

1. Define the variables
2. State the null hypothesis
3. State the alternative hypothesis

STEP 3

Let's define what $p_1$ and $p_2$ represent.
We're given that $p_1$ is the high school graduation rate in the United States.
Let's define $p_2$ as the high school graduation rate in Europe.
This helps us keep track of what we're comparing!

STEP 4

The null hypothesis ( $H_0$ ) is the statement we're trying to disprove.
It usually represents the status quo or the assumption of no difference.
In this case, the null hypothesis would be that the high school graduation rates in the US and Europe are the same.
We can write this mathematically as: $H_0: p_1 = p_2$

STEP 5

The alternative hypothesis ( $H_1$ ) is what we think is actually true.
The research study concludes that the US graduation rate is higher than Europe's.
So, our alternative hypothesis is: $H_1: p_1 > p_2$ This means we believe $p_1$ is greater than $p_2$ .

STEP 6

Null Hypothesis: $H_0: p_1 = p_2$ Alternative Hypothesis: $H_1: p_1 > p_2$

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Studdy Solution

STEP 1

STEP 2

1. Define the variables
2. State the null hypothesis
3. State the alternative hypothesis

STEP 3

Let's define what $p_1$ and $p_2$ represent.
We're given that $p_1$ is the high school graduation rate in the United States.
Let's define $p_2$ as the high school graduation rate in Europe.
This helps us keep track of what we're comparing!

STEP 4

STEP 5

The alternative hypothesis ( $H_1$ ) is what we think is actually true.
The research study concludes that the US graduation rate is higher than Europe's.
So, our alternative hypothesis is: $H_1: p_1 > p_2$ This means we believe $p_1$ is greater than $p_2$ .

STEP 6

Null Hypothesis: $H_0: p_1 = p_2$ Alternative Hypothesis: $H_1: p_1 > p_2$

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Studdy Solution

STEP 1

STEP 2

1. Define the variables2. State the null hypothesis3. State the alternative hypothesis

STEP 3

Let's **define** what p1p_1p1​ and p2p_2p2​ represent.We're given that p1p_1p1​ is the high school graduation rate in the United States.Let's define p2p_2p2​ as the high school graduation rate in Europe.This helps us keep track of what we're comparing!

STEP 4

STEP 5

The **alternative hypothesis** (H1H_1H1​) is what we think is *actually true*.The research study concludes that the US graduation rate is *higher* than Europe's.So, our alternative hypothesis is: H1:p1>p2H_1: p_1 > p_2H1​:p1​>p2​ This means we believe p1p_1p1​ is greater than p2p_2p2​.

STEP 6

Null Hypothesis: H0:p1=p2H_0: p_1 = p_2H0​:p1​=p2​ Alternative Hypothesis: H1:p1>p2H_1: p_1 > p_2H1​:p1​>p2​

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1. Define the variables
2. State the null hypothesis
3. State the alternative hypothesis

Let's define what $p_1$ and $p_2$ represent.
We're given that $p_1$ is the high school graduation rate in the United States.
Let's define $p_2$ as the high school graduation rate in Europe.
This helps us keep track of what we're comparing!

The alternative hypothesis ( $H_1$ ) is what we think is actually true.
The research study concludes that the US graduation rate is higher than Europe's.
So, our alternative hypothesis is: $H_1: p_1 > p_2$ This means we believe $p_1$ is greater than $p_2$ .

Null Hypothesis: $H_0: p_1 = p_2$ Alternative Hypothesis: $H_1: p_1 > p_2$