ne-sample z-test using the given sample mean, population standard deviation, and sample size, with a significance level (alpha) of 0.10.

To perform a one-sample z-test, we will follow the steps outlined below:

1. ### Break Down the Problem

1. Identify the sample mean ($\bar{x}$).
2. Identify the population standard deviation ($\sigma$).
3. Identify the sample size ($n$).
4. Identify the significance level (alpha = 0.10).

2. ### Relevant Concepts

• The formula for the z-test statistic is given by:

$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$

Where:

• $\bar{x}$ = sample mean
• $\mu$ = population mean (this should be defined in the problem, but is not provided in your question)
• $\sigma$ = population standard deviation
• $n$ = sample size

3. ### Analysis and Detail

Assuming you have specific values for $\bar{x}$, $\sigma$, $n$, and $\mu$ (the population mean you are testing against), you would substitute them into the z-test formula above to calculate the z-value.

4. ### Verify and Summarize

• Once you have calculated the z-value, you would compare it to the critical z-value for a significance level (alpha) of 0.10.
• For a two-tailed test, the critical z-values for alpha = 0.10 are approximately $-1.645$ and $1.645$.
• If the calculated z-value falls beyond these critical z-values, you reject the null hypothesis.

Final Answer

Without the specific values for the sample mean, population mean, sample size, and standard deviation, I can't calculate a precise answer. Please provide these values to proceed with the computation or verify your hypothesis.