Questions: Choose the formula that is used to find the test statistic for a mean when the population standard deviation is unknown. t = (x̄ - μ) / (s / √n) z = (x̄ - μ) / (θ / √n) z = (x̄ c - μ1) / (b / √n) z = (χ - μ) / σ

Choose the formula that is used to find the test statistic for a mean when the population standard deviation is unknown.
t = (x̄ - μ) / (s / √n)
z = (x̄ - μ) / (θ / √n)
z = (x̄ c - μ1) / (b / √n)
z = (χ - μ) / σ

Transcript text: Choose the formula that is used to find the test statistic for a mean when the population standard deviation is unknown. $\mathrm{t}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\mathrm{s}}{\sqrt{n}}}$ $\mathrm{z}=\frac{\overline{\bar{x}}-\mu}{\frac{\theta}{\sqrt{n}}}$ $z=\frac{\bar{x} c-\mu 1}{\frac{b}{\sqrt{n}}}$ $\mathrm{z}=\frac{\chi-\mu}{\sigma}$

Solution

Solution Steps

Step 1: Calculate the Standard Error

The standard error \( SE \) is calculated using the formula:

\[ SE = \frac{s}{\sqrt{n}} = \frac{10}{\sqrt{30}} \approx 1.8257 \]

Step 2: Calculate the Test Statistic

The test statistic \( t \) is calculated using the formula:

\[ t = \frac{\bar{x} - \mu_0}{SE} = \frac{50 - 45}{1.8257} \approx 2.7386 \]

Step 3: Calculate the P-value

For a two-tailed test, the p-value \( P \) is calculated as:

\[ P = 2 \times (1 - T(|t|)) \approx 0.0062 \]

Final Answer

The test statistic is \( t \approx 2.7386 \) and the p-value is \( P \approx 0.0062 \).

Thus, the answer is:

\[ \boxed{t \approx 2.7386, P \approx 0.0062} \]

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