Math / Data & Statistics

Questionh. Interpret the level of significance in the context of the study. - There is a $10 \%$ chance that there is a difference in the proportion of blonde and brunette college students who have a boyfriend. If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 638 blonde college students and 791 brunette college students are surveyed then there would be a $10 \%$ chance that we would end up falsely concuding that the population proportion of blonde college students who have a boyfriend is greater than the population proportion of brunette college students who have a boyfriend If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 638 blonde college students and 791 brunette college students are surveyed then there would be a $10 \%$ chance that we would end up falsely concuding that the proportion of these surveyed blonde and brunette college students who have a boyfriend differ from each other. There is a $10 \%$ chance that you will never get a boyfriend unless you dye your hair blonde.

Studdy Solution

STEP 1

What is this asking? If we assume there's no difference between blonde and brunette students having boyfriends, how often would our study incorrectly say there is a difference? Watch out! Don't mix up "there's no difference" with "there is a difference"!
Also, we're focusing on a false conclusion, not a true one.

STEP 2

1. Understand Significance Level
2. Interpret in Context

STEP 3

The significance level, often shown as $\alpha$ , tells us the risk we're willing to take of making a wrong call, specifically saying there's a difference when there really isn't!
Here, $\alpha = 0.10$ or 10%.

STEP 4

This 10% is the chance of a false positive.
It's like a fire alarm going off when there's no fire.
In our case, it means concluding there's a boyfriend difference between hair colors when there really isn't.

STEP 5

We're asking: If blonde and brunette students are equally likely to have boyfriends, what's the chance our study wrongly says they aren't?

STEP 6

That chance is precisely our significance level, which is 10%.
It's the risk we take of seeing a difference where none exists.

STEP 7

The correct option is the one that says if we did the study again with the same number of students (638 blondes and 791 brunettes), there's a 10% chance we'd falsely conclude that blondes are more likely to have boyfriends than brunettes.

STEP 8

The correct answer is the second option: "If the percent of all blonde college students who have a boyfriend is the same as the percent of all brunette college students who have a boyfriend and if another 638 blonde college students and 791 brunette college students are surveyed then there would be a 10% chance that we would end up falsely concluding that the population proportion of blonde college students who have a boyfriend is greater than the population proportion of brunette college students who have a boyfriend."

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Studdy Solution

STEP 1

STEP 2

1. Understand Significance Level
2. Interpret in Context

STEP 3

The significance level, often shown as $\alpha$ , tells us the risk we're willing to take of making a wrong call, specifically saying there's a difference when there really isn't!
Here, $\alpha = 0.10$ or 10%.

STEP 4

This 10% is the chance of a false positive.
It's like a fire alarm going off when there's no fire.
In our case, it means concluding there's a boyfriend difference between hair colors when there really isn't.

STEP 5

We're asking: If blonde and brunette students are equally likely to have boyfriends, what's the chance our study wrongly says they aren't?

STEP 6

That chance is precisely our significance level, which is 10%.
It's the risk we take of seeing a difference where none exists.

STEP 7

The correct option is the one that says if we did the study again with the same number of students (638 blondes and 791 brunettes), there's a 10% chance we'd falsely conclude that blondes are more likely to have boyfriends than brunettes.

STEP 8

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Studdy Solution

STEP 1

STEP 2

1. Understand Significance Level2. Interpret in Context

STEP 3

The significance level, often shown as α\alphaα, tells us the risk we're willing to take of making a wrong call, specifically saying there's a difference when there really isn't!Here, α=0.10\alpha = 0.10α=0.10 or **10%**.

STEP 4

This **10%** is the chance of a *false positive*.It's like a fire alarm going off when there's no fire.In our case, it means concluding there's a boyfriend difference between hair colors when there really isn't.

STEP 5

We're asking: If blonde and brunette students are *equally* likely to have boyfriends, what's the chance our study *wrongly* says they *aren't*?

STEP 6

That chance is precisely our significance level, which is **10%**.It's the risk we take of seeing a difference where none exists.

STEP 7

The correct option is the one that says if we did the study again with the same number of students (**638 blondes** and **791 brunettes**), there's a **10%** chance we'd *falsely* conclude that blondes are more likely to have boyfriends than brunettes.

STEP 8

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Start learning now

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1. Understand Significance Level
2. Interpret in Context

The significance level, often shown as $\alpha$ , tells us the risk we're willing to take of making a wrong call, specifically saying there's a difference when there really isn't!
Here, $\alpha = 0.10$ or 10%.

This 10% is the chance of a false positive.
It's like a fire alarm going off when there's no fire.
In our case, it means concluding there's a boyfriend difference between hair colors when there really isn't.

We're asking: If blonde and brunette students are equally likely to have boyfriends, what's the chance our study wrongly says they aren't?

That chance is precisely our significance level, which is 10%.
It's the risk we take of seeing a difference where none exists.

The correct option is the one that says if we did the study again with the same number of students (638 blondes and 791 brunettes), there's a 10% chance we'd falsely conclude that blondes are more likely to have boyfriends than brunettes.