Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below.

Original​ claim: More than 44​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.0131.

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Part 1

a. State a conclusion about the null hypothesis.​ (Reject Upper H 0 or fail to reject Upper H 0​.) Choose the correct answer below.

A.

Reject Upper H 0 because the​ P-value is greater than alpha.

B.

Fail to reject Upper H 0 because the​ P-value is less than or equal to alpha.

C.

Fail to reject Upper H 0 because the​ P-value is greater than alpha.

D.

Reject Upper H 0 because the​ P-value is less than or equal to alpha.

To determine the correct conclusion regarding the null hypothesis \( H_0 \), we need to compare the given \( P \)-value (0.0131) with the significance level \( \alpha \) (0.05).

The decision rule is as follows:
- **Reject \( H_0 \)** if the \( P \)-value is **less than or equal to** \( \alpha \).
- **Fail to reject \( H_0 \)** if the \( P \)-value is **greater than** \( \alpha \).

Given:
- \( P \)-value = 0.0131
- \( \alpha = 0.05 \)

Since \( 0.0131 < 0.05 \), we **reject \( H_0 \)**.

### Conclusion:
The correct answer is:
**D. Reject \( H_0 \) because the \( P \)-value is less than or equal to \( \alpha \).**

Would you like further details on interpreting \( P \)-values or have any other questions?

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Here are some related questions you might find helpful:
1. What is the meaning of a significance level in hypothesis testing?
2. How does the \( P \)-value relate to the likelihood of observing the sample result under the null hypothesis?
3. What are the possible outcomes and implications of rejecting \( H_0 \)?
4. How would the conclusion change if the \( P \)-value were 0.06 instead of 0.0131?
5. Why is it important to set a significance level before conducting a hypothesis test?

**Tip:** Always compare the \( P \)-value with the significance level to determine whether to reject the null hypothesis; this comparison is fundamental in hypothesis testing.

Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below.

Original​ claim: More than 44​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.0131.

Part 1
a. State a conclusion about the null hypothesis.​ (Reject Upper H 0 or fail to reject Upper H 0​.) Choose the correct answer below.

A.
Reject Upper H 0 because the​ P-value is greater than alpha.
B.
Fail to reject Upper H 0 because the​ P-value is less than or equal to alpha.
C.
Fail to reject Upper H 0 because the​ P-value is greater than alpha.
D.
Reject Upper H 0 because the​ P-value is less than or equal to alpha.

Learn how to interpret the P-value in hypothesis testing with this problem involving a significance level of 0.05. The problem concludes that the null hypothesis is rejected because the P-value (0.0131) is less than the significance level. Suitable for high school students studying hypothesis testing in statistics.

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