Questions: Find the P -value for this hypothesis test. P -value = (Round to three decimal places as needed.)

Find the P -value for this hypothesis test. P -value = (Round to three decimal places as needed.)
Transcript text: Find the P -value for this hypothesis test. P -value $=$ $\square$ (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Calculate the Standard Error (SE)

The Standard Error is calculated using the formula:

\[ SE = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}} = \sqrt{\frac{701.8}{5} + \frac{1010.0}{5}} = 18.503 \]

Step 2: Calculate the Test Statistic (t)

The test statistic \( t \) is computed as follows:

\[ t = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{51.6 - 54.0}{18.503} = -0.13 \]

Step 3: Calculate the Degrees of Freedom (df)

The degrees of freedom are calculated using the formula:

\[ df = \frac{\left(\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}\right)^2}{\frac{\left(\frac{s_1^2}{n_1}\right)^2}{n_1 - 1} + \frac{\left(\frac{s_2^2}{n_2}\right)^2}{n_2 - 1}} = \frac{117210.37}{15126.232} = 7.749 \]

Step 4: Calculate the P-value

The P-value is determined using the formula:

\[ P = 2(1 - T(|t|)) = 2(1 - T(0.13)) = 0.9 \]

Final Answer

The P-value for this hypothesis test is

\[ \boxed{0.900} \]

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