To determine the test statistic, we need more context about the hypotheses and the type of test you're conducting. Here's how you can approach it step-by-step:

1. Identify the type of test:

• Are you performing a z-test, t-test, chi-square test, or another statistical test?
• This depends on the nature of the data, sample size, and whether population parameters (like standard deviation) are known.

2. Specify the hypotheses:

• Null hypothesis ($H_0$): Often states no effect or no difference.
• Alternative hypothesis ($H_a$): Indicates the effect or difference you're testing.

3. Calculate the test statistic:

• For a z-test:
  $z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$
  Where:

  • $\bar{x}$ = sample mean
  • $\mu$ = population mean under $H_0$
  • $\sigma$ = population standard deviation
  • $n$ = sample size

• For a t-test:
  $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$
  Where:

  • $s$ = sample standard deviation (used if $\sigma$ is unknown).

• For a chi-square test:
  $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$
  Where:

  • $O_i$ = observed frequencies
  • $E_i$ = expected frequencies.

• For an ANOVA F-test:
  $F = \frac{\text{Between-group variance}}{\text{Within-group variance}}$

4. Plug in your values:

Once you have the data, substitute the values into the appropriate formula.

If you provide additional details about the hypotheses, data, or test type, I can compute or guide you through the calculation in detail!

---

Would you like to share specifics so we can proceed?
Here are 5 questions to clarify:

1. What is the type of test (e.g., z-test, t-test, chi-square, etc.)?
2. Do you have the hypotheses ($H_0$ and $H_a$)?
3. What data or parameters are provided (means, standard deviations, sample sizes, etc.)?
4. Are you working with one sample or multiple samples?
5. Is this a one-tailed or two-tailed test?

Tip: Clearly define your null and alternative hypotheses before proceeding with calculations to avoid errors.