Questions: (c) State the appropriate null and alternate hypotheses. H0: μ<15 H1: μ>15 (d) Compute the value of the test statistic. Round the answer to at least two decimal places. z=

(c) State the appropriate null and alternate hypotheses.
H0: μ<15
H1: μ>15

(d) Compute the value of the test statistic. Round the answer to at least two decimal places.
z=

Transcript text: (c) State the appropriate null and alternate hypotheses. \[ \begin{array}{l} H_{0}: \mu<15 \\ H_{1}: \mu>15 \end{array} \] (d) Compute the value of the test statistic. Round the answer to at least two decimal places. \[ z= \]

Solution

Solution Steps

Step 1: Calculate the Standard Error

The standard error \( SE \) is calculated using the formula: \[ SE = \frac{\sigma}{\sqrt{n}} = \frac{2.5}{\sqrt{30}} \approx 0.46 \]

Step 2: Compute the Test Statistic

The test statistic \( Z_{test} \) is computed using the formula: \[ Z_{test} = \frac{\bar{x} - \mu_0}{SE} = \frac{16 - 15}{0.46} \approx 2.19 \]

Step 3: Determine the P-value

For a right-tailed test, the P-value is calculated as: \[ P = 1 - T(z) \approx 0.01 \]

Step 4: State the Test Statistic

The calculated test statistic is: \[ Z_{test} = 2.19 \]

Final Answer

The null and alternate hypotheses are: \[ \begin{array}{l} H_{0}: \mu < 15 \\ H_{1}: \mu > 15 \end{array} \] The test statistic is \( \boxed{2.19} \).

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