cartons should have 1000ml
sample of 50 cartons
sample mean is 995ml

stdev is 25ml

alpha 5%
calculate the test statistic

To calculate the test statistic for this problem, we can use the formula for a **one-sample Z-test** for means. The formula is:

\[
Z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]

Where:
- \(\bar{x}\) is the sample mean (995 ml),
- \(\mu\) is the population mean (1000 ml),
- \(\sigma\) is the population standard deviation (25 ml),
- \(n\) is the sample size (50),
- \(Z\) is the test statistic.

Let's calculate this:

\[
Z = \frac{995 - 1000}{\frac{25}{\sqrt{50}}}
\]

Now, let's compute it step-by-step.The calculated test statistic (Z-value) is approximately \(-1.41\).

Would you like further details on the interpretation or additional assistance with hypothesis testing?

Here are 5 related questions you might find helpful:
1. How do we interpret the Z-value in this context?
2. What is the critical Z-value for a 5% significance level?
3. How do we determine if we should reject the null hypothesis?
4. How would the test change if the sample size were larger?
5. What is the relationship between the sample mean and population mean in hypothesis testing?

**Tip:** A negative Z-value indicates that the sample mean is below the population mean.

Cartons should have 1000ml. Sample of 50 cartons has a sample mean of 995ml and a standard deviation of 25ml. Alpha is 5%. Calculate the test statistic.

Learn how to calculate the Z-value for a hypothesis test comparing a sample mean of 995ml with a population mean of 1000ml. This example uses a one-sample Z-test with a sample size of 50 and a standard deviation of 25ml. Suitable for college-level statistics.

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