Question

A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 401 gram setting. It is believed that the machine is underfilling the bags. A 33 bag sample had a mean of 394 grams with a standard deviation of 21. Assume the population is normally distributed. A level of significance of 0.05 will be used. Specify the type of hypothesis test.

Answer 1

The appropriate hypothesis test for determining if a potato chip bag filling machine is underfilling is a one-tailed t-test for the mean, using a level of significance of 0.05.

Step-by-step explanation:

The student is asking for the type of hypothesis test needed to determine whether a potato chip bag filling machine is correctly calibrated at the 401-gram setting, given a sample mean and standard deviation. Since the concern is that the machine is underfilling, we will conduct a one-tailed t-test for the mean (a single-sample t-test) because the population standard deviation is unknown and the sample size is less than 30, which requires using the t-distribution.

The null hypothesis (H₀) states that the mean weight of the bags is equal to 401 grams, and the alternative hypothesis (H₁) states that the mean weight is less than 401 grams. The level of significance is set at 0.05. This dictates that if the test statistic falls within the lower 5% of the t-distribution, we will reject the null hypothesis and conclude that there is evidence to suggest the machine is underfilling the bags.