Suppose there is a claim that a certain population has a mean, μ, that is different than 8 . You

Hi, I'm David and I'm here to have the answer in your question. Now let me bring up your questio

solution. So in the question, unknown hypothesis is merely 9, alternative hypothesis is merely d

Let's solve the given question. So we are having H0 mu1 minus mu2 greater than equals to 0. H1 i

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From the given information we have degrees of freedom is equal to 2. Level of significance alpha

Question

Suppose there is a claim that a certain population has a mean, \( \mu \), that is different than 8 . You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, \( H_{0} \), and the alternative hypothesis, \( H_{1} \), as follows. \[ \begin{array}{l} H_{0}: \mu=8 \\ H_{1}: \mu \neq 8 \end{array} \] Suppose you also know the following information. The value of the test statistic based on the sample is -1.728 (rounded to 3 decimal places). The \( p \)-value is 0.084 (rounded to 3 decimal places). (a) Complete the steps below for this hypothesis test. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. One-tailed Two-tailed Step 2: Enter the test statistic. (Round to 3 decimal places.) \( \square \) Step 3: Shade the area represented by the \( p \)-value. Step 4: Enter the p-value. (Round to 3 decimal places.) \( \square \) (b) Based on your answer to part (a), which statement below is true? Since the \( p \)-value is less than (or equal to) the level of significance, the null hypothesis is rejected. Since the \( p \)-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. Since the \( p \)-value is greater than the level of significance, the null hypothesis is rejected. Since the \( p \)-value is greater than the level of significance, the null hypothesis is not rejected.

          Suppose there is a claim that a certain population has a mean, \( \mu \), that is different than 8 . You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, \( H_{0} \), and the alternative hypothesis, \( H_{1} \), as follows.
\[
\begin{array}{l}
H_{0}: \mu=8 \\
H_{1}: \mu \neq 8
\end{array}
\]

Suppose you also know the following information.
The value of the test statistic based on the sample is -1.728 (rounded to 3 decimal places).
The \( p \)-value is 0.084 (rounded to 3 decimal places).
(a) Complete the steps below for this hypothesis test.
Standard Normal Distribution
Step 1: Select one-tailed or two-tailed.
One-tailed
Two-tailed
Step 2: Enter the test statistic. (Round to 3 decimal places.)
\( \square \)
Step 3: Shade the area represented by the \( p \)-value.

Step 4: Enter the p-value. (Round to 3 decimal places.)
\( \square \)
(b) Based on your answer to part (a), which statement below is true?
Since the \( p \)-value is less than (or equal to) the level of significance, the null hypothesis is rejected.
Since the \( p \)-value is less than (or equal to) the level of significance, the null hypothesis is not rejected.
Since the \( p \)-value is greater than the level of significance, the null hypothesis is rejected.
Since the \( p \)-value is greater than the level of significance, the null hypothesis is not rejected.

Suppose there is a claim that a certain population has a mean, μ, that is different than 8 . You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, H0, and the alternative hypothesis, H1, as follows.

H0: μ=8

H1: μ≠ 8

Suppose you also know the following information.
The value of the test statistic based on the sample is -1.728 (rounded to 3 decimal places).
The p-value is 0.084 (rounded to 3 decimal places).
(a) Complete the steps below for this hypothesis test.
Standard Normal Distribution
Step 1: Select one-tailed or two-tailed.
One-tailed
Two-tailed
Step 2: Enter the test statistic. (Round to 3 decimal places.)
□
Step 3: Shade the area represented by the p-value.

Step 4: Enter the p-value. (Round to 3 decimal places.)
□
(b) Based on your answer to part (a), which statement below is true?
Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected.
Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected.
Since the p-value is greater than the level of significance, the null hypothesis is rejected.
Since the p-value is greater than the level of significance, the null hypothesis is not rejected.

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