Questions: What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=0.27? (Do not round your answer; compute your answer using a value from the table below.) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.540 0.544 0.548 0.552 0.556 0.560 0.564 0.567 0.571 0.575 0.2 0.579 0.583 0.587 0.591 0.595 0.599 0.603 0.606 0.610 0.614 0.3 0.618 0.622 0.626 0.629 0.633 0.637 0.641 0.644 0.648 0.652 0.4 0.655 0.659 0.663 0.666 0.670 0.674 0.677 0.681 0.684 0.688 0.5 0.691 0.695 0.698 0.702 0.705 0.709 0.712 0.716 0.719 0.722

What is the p-value of a two-tailed one-mean hypothesis test, with a test statistic of z0=0.27? (Do not round your answer; compute your answer using a value from the table below.) z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.540 0.544 0.548 0.552 0.556 0.560 0.564 0.567 0.571 0.575 0.2 0.579 0.583 0.587 0.591 0.595 0.599 0.603 0.606 0.610 0.614 0.3 0.618 0.622 0.626 0.629 0.633 0.637 0.641 0.644 0.648 0.652 0.4 0.655 0.659 0.663 0.666 0.670 0.674 0.677 0.681 0.684 0.688 0.5 0.691 0.695 0.698 0.702 0.705 0.709 0.712 0.716 0.719 0.722
Transcript text: Question What is the $p$-value of a two-tailed one-mean hypothesis test, with a test statistic of $z_{0}=0.27$ ? (Do not round your answer; compute your answer using a value from the table below.) \begin{tabular}{c|cccccccccc} z & $\mathbf{0 . 0 0}$ & $\mathbf{0 . 0 1}$ & $\mathbf{0 . 0 2}$ & $\mathbf{0 . 0 3}$ & $\mathbf{0 . 0 4}$ & $\mathbf{0 . 0 5}$ & $\mathbf{0 . 0 6}$ & $\mathbf{0 . 0 7}$ & $\mathbf{0 . 0 8}$ & $\mathbf{0 . 0 9}$ \\ \hline $\mathbf{0 . 1}$ & 0.540 & 0.544 & 0.548 & 0.552 & 0.556 & 0.560 & 0.564 & 0.567 & 0.571 & 0.575 \\ $\mathbf{0 . 2}$ & 0.579 & 0.583 & 0.587 & 0.591 & 0.595 & 0.599 & 0.603 & 0.606 & 0.610 & 0.614 \\ $\mathbf{0 . 3}$ & 0.618 & 0.622 & 0.626 & 0.629 & 0.633 & 0.637 & 0.641 & 0.644 & 0.648 & 0.652 \\ $\mathbf{0 . 4}$ & 0.655 & 0.659 & 0.663 & 0.666 & 0.670 & 0.674 & 0.677 & 0.681 & 0.684 & 0.688 \\ $\mathbf{0 . 5}$ & 0.691 & 0.695 & 0.698 & 0.702 & 0.705 & 0.709 & 0.712 & 0.716 & 0.719 & 0.722 \end{tabular} Provide your answer below:
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Solution

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Solution Steps

To find the $p$-value for a two-tailed one-mean hypothesis test with a given test statistic $z_0 = 0.27$, we need to:

  1. Use the standard normal distribution to find the cumulative probability corresponding to $z_0 = 0.27$.
  2. Since it is a two-tailed test, calculate the $p$-value as twice the area in the tail beyond the absolute value of the test statistic.
Step 1: Calculate the Cumulative Probability for \( z_0 \)

Given the test statistic \( z_0 = 0.27 \), we first find the cumulative probability from the standard normal distribution: \[ \text{cumulative\_prob} = 0.6064 \]

Step 2: Calculate the Area in the Tail

For a two-tailed test, we need to calculate the area in the tail beyond the absolute value of the test statistic. This is given by: \[ \text{tail\_area} = 1 - \text{cumulative\_prob} = 1 - 0.6064 = 0.3936 \]

Step 3: Calculate the \( p \)-value

Since it is a two-tailed test, the \( p \)-value is twice the area in the tail: \[ p\text{-value} = 2 \times \text{tail\_area} = 2 \times 0.3936 = 0.7872 \]

Final Answer

\[ \boxed{p\text{-value} = 0.7872} \]

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