Math / Data & Statistics

QuestionA hypothesis test produced a $p$ -value of 0.09981 . If the test was conducted at the significance level $\alpha=0.09$ , which of the following is correct about the result? Reject $H_{0}$ ; neither Type I error nor Type II error is possible. Do not reject $H_{0}$ ; a Type II error is possible. Reject $H_{0}$ ; a Type I error is possible. Reject $H_{1}$ ; a Type I error is possible. Do not reject $H_{1}$ ; a Type II error is possible.

Studdy Solution

STEP 1

What is this asking? Should we reject the null hypothesis $H_0$ based on the given p-value and significance level, and what type of error is possible? Watch out! Don't mix up Type I and Type II errors!
A Type I error happens when you reject a true null hypothesis, while a Type II error happens when you fail to reject a false null hypothesis.

STEP 2

1. Compare p-value and significance level.
2. Determine rejection.
3. Identify possible errors.

STEP 3

Alright, let's compare our p-value, which is $0.09981$ , with our significance level $\alpha$ , which is $0.09$ .
Remember, the p-value tells us the probability of observing our data, or more extreme data, if the null hypothesis is actually true.

STEP 4

Is $0.09981$ less than or equal to $0.09$ ?
Nope! $0.09981$ is greater than $0.09$ .
This means the probability of observing our data under the null hypothesis is relatively high.

STEP 5

Since our p-value ( $0.09981$ ) is greater than our significance level ( $0.09$ ), we do not reject the null hypothesis $H_0$ .
We don't have enough evidence to reject it!

STEP 6

Since we did not reject $H_0$ , we could have made a Type II error.
This would mean that the null hypothesis is actually false, but we failed to reject it based on our data.
A Type I error is only possible when we reject the null hypothesis, which we didn't do here.

STEP 7

We do not reject $H_0$ , and a Type II error is possible.

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Studdy Solution

STEP 1

STEP 2

1. Compare p-value and significance level.
2. Determine rejection.
3. Identify possible errors.

STEP 3

Alright, let's compare our p-value, which is $0.09981$ , with our significance level $\alpha$ , which is $0.09$ .
Remember, the p-value tells us the probability of observing our data, or more extreme data, if the null hypothesis is actually true.

STEP 4

Is $0.09981$ less than or equal to $0.09$ ?
Nope! $0.09981$ is greater than $0.09$ .
This means the probability of observing our data under the null hypothesis is relatively high.

STEP 5

Since our p-value ( $0.09981$ ) is greater than our significance level ( $0.09$ ), we do not reject the null hypothesis $H_0$ .
We don't have enough evidence to reject it!

STEP 6

Since we did not reject $H_0$ , we could have made a Type II error.
This would mean that the null hypothesis is actually false, but we failed to reject it based on our data.
A Type I error is only possible when we reject the null hypothesis, which we didn't do here.

STEP 7

We do not reject $H_0$ , and a Type II error is possible.

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Studdy Solution

STEP 1

STEP 2

1. Compare p-value and significance level.2. Determine rejection.3. Identify possible errors.

STEP 3

Alright, let's **compare** our **p-value**, which is 0.099810.099810.09981, with our **significance level** α\alphaα, which is 0.090.090.09.Remember, the p-value tells us the probability of observing our data, or more extreme data, if the null hypothesis is actually true.

STEP 4

Is 0.099810.099810.09981 less than or equal to 0.090.090.09?Nope! 0.099810.099810.09981 is **greater than** 0.090.090.09.This means the probability of observing our data under the null hypothesis is relatively high.

STEP 5

Since our **p-value** (0.099810.099810.09981) is **greater than** our **significance level** (0.090.090.09), we **do not reject** the **null hypothesis** H0H_0H0​.We don't have enough evidence to reject it!

STEP 6

Since we **did not reject** H0H_0H0​, we could have made a **Type II error**.This would mean that the null hypothesis is actually false, but we failed to reject it based on our data.A **Type I error** is only possible when we reject the null hypothesis, which we didn't do here.

STEP 7

We **do not reject** H0H_0H0​, and a **Type II error** is possible.

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1. Compare p-value and significance level.
2. Determine rejection.
3. Identify possible errors.

Alright, let's compare our p-value, which is $0.09981$ , with our significance level $\alpha$ , which is $0.09$ .
Remember, the p-value tells us the probability of observing our data, or more extreme data, if the null hypothesis is actually true.

Is $0.09981$ less than or equal to $0.09$ ?
Nope! $0.09981$ is greater than $0.09$ .
This means the probability of observing our data under the null hypothesis is relatively high.

Since our p-value ( $0.09981$ ) is greater than our significance level ( $0.09$ ), we do not reject the null hypothesis $H_0$ .
We don't have enough evidence to reject it!

Since we did not reject $H_0$ , we could have made a Type II error.
This would mean that the null hypothesis is actually false, but we failed to reject it based on our data.
A Type I error is only possible when we reject the null hypothesis, which we didn't do here.

We do not reject $H_0$ , and a Type II error is possible.