A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 433433 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 2828 bag sample had a mean of 435435 grams with a variance of 625625. Assume the population is normally distributed. A level of significance of 0.10.1 will be used. Specify the type of hypothesis test.

In this scenario, the manufacturer wants to determine whether the bag filling machine is either **underfilling** or **overfilling** the bags. This suggests we will be performing a **two-tailed test** because deviations in both directions (less than or greater than 433 grams) are of interest.

### Step 1: Set Up the Hypotheses

Since we are testing whether the machine is either underfilling or overfilling, we will set up a two-tailed test with the following hypotheses:

- **Null Hypothesis** (\( H_0 \)): The machine is filling the bags correctly, i.e., the mean is 433 grams.
  \[
  H_0: \mu = 433
  \]
- **Alternative Hypothesis** (\( H_A \)): The machine is either underfilling or overfilling the bags, i.e., the mean is different from 433 grams.
  \[
  H_A: \mu \neq 433
  \]

### Step 2: Type of Test

Now, let's evaluate the type of hypothesis test to be conducted. The following conditions apply:
- We are given a **sample size** of \( n = 28 \), which is moderate.
- The **sample mean** is \( \bar{x} = 435 \) grams.
- The **sample variance** is \( s^2 = 625 \), so the **sample standard deviation** \( s = \sqrt{625} = 25 \) grams.
- We do not know the population standard deviation, but we assume the population is normally distributed.

Since the population standard deviation is unknown and the sample size is less than 30 (though approaching it), the most appropriate test is a **one-sample t-test**. 

### Step 3: Determine the Test Statistic

The formula for the t-test statistic is:

\[
t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}
\]

Where:
- \( \bar{x} = 435 \) is the sample mean.
- \( \mu_0 = 433 \) is the hypothesized population mean.
- \( s = 25 \) is the sample standard deviation.
-

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 433 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 28 bag sample had a mean of 435 grams with a variance of 625. Assume the population is normally distributed. A level of significance of 0.1 will be used. Specify the type of hypothesis test.

Determine whether a bag filling machine is overfilling or underfilling banana chip bags with a sample mean of 435 grams, using a 28-bag sample, a significance level of 0.1, and a two-tailed t-test. Learn how to perform this hypothesis test with detailed steps.

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