Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 437 gram setting. It is believed that the machine is underfiling the bags. A 32 bag sample had a mean of 429 grams with a standard deviation of 25. Assume the population is normally distributed. A level of significance of 0.1 will be used. State the null and alternative hypotheses.

Answer 1

The null hypothesis is that the mean weight of the bags is 437 grams (H0: μ = 437), and the alternative hypothesis is that the mean weight is less than 437 grams (Ha: μ < 437). A significance level of 0.1 is used for the test.

Step-by-step explanation:

To assess whether the bag filling machine is operating correctly at the 437 gram setting, we need to establish the null and alternative hypotheses for a one-sample mean test (t-test) since we are dealing with a sample mean and an assumed normal population distribution. The null hypothesis (H0) states that the machine is filling the bags correctly, meaning the mean weight of the bags is 437 grams. The alternative hypothesis (Ha) suggests that the machine is underfilling the bags, and thus the mean weight would be less than 437 grams.

In formal terms, the hypotheses would be stated as:

• Null hypothesis (H0): The mean weight of the bags μ equals 437 grams, or μ = 437.
• Alternative hypothesis (Ha): The mean weight of the bags μ is less than 437 grams, or μ < 437.

A significance level of 0.1 means we have a 10% chance of rejecting the null hypothesis if it is true (Type I error).