A flourmill is concerned that new machinery is not filling bags correctly. The bags are supposed to have a population mean weight of 500 grams. A random sample of 147 bags of flour has a mean weight of 541 grams and a standard deviation of 3.3 grams.  Give the value of the calculated test statistic, to two decimal places

To calculate the test statistic for this situation, we will use the formula for the Z-test when the population standard deviation is unknown, but a sample standard deviation is given:

\[
Z = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}}
\]

Where:
- \(\bar{X}\) is the sample mean (541 grams),
- \(\mu\) is the population mean (500 grams),
- \(s\) is the sample standard deviation (3.3 grams),
- \(n\) is the sample size (147 bags).

Let's calculate the test statistic.The value of the calculated test statistic is **150.64**.

Would you like more details or have any questions about this? Here are some related questions to expand your understanding:

1. How do you interpret the result of the Z-test in this context?
2. What is the significance of using a Z-test over a t-test here?
3. How would you determine if the machinery is significantly overfilling the bags?
4. What is the critical Z-value for a 95% confidence level in a one-tailed test?
5. How would increasing the sample size affect the test statistic?

**Tip**: A large test statistic like this indicates a significant difference between the sample mean and the population mean.

A flourmill is concerned that new machinery is not filling bags correctly. The bags are supposed to have a population mean weight of 500 grams. A random sample of 147 bags of flour has a mean weight of 541 grams and a standard deviation of 3.3 grams. Give the value of the calculated test statistic, to two decimal places.

Find out how to calculate the Z-test statistic for a flourmill's machinery checking the weight of bags. With a population mean of 500 grams and a sample mean of 541 grams from 147 bags, learn how a standard deviation of 3.3 grams leads to a test statistic of 150.64. Understand the process behind the Z-test and hypothesis testing.

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