Question

Potato Chip Quality Control. NDC Technology’s MM710e On-Line Snacks Gauge rapidly measures surface brownness of potato chips just before packaging. This allows for a high degree of control over this important characteristic of a potato chip; chips that are too brown are overfried, and chips that are not sufficiently brown are underfried. A potato chip manufacturer is now using the MM710e to assess the quality of the chips it produces; one of this manufacturer’s goals is to produce less than 1 overfried chip in every 1000 chips. In a recent random sample of 111,667 chips taken from the production lines of the manufacturer’s production facilities nationwide, the MM710e found 98 overfried chips. Conduct a hypothesis test to determine if the sample data indicates the manufacturer is meeting its goal for overfried chips at � = .05 .

Answer 1

To determine if the potato chip manufacturer is meeting its goal for overfried chips, a hypothesis test can be conducted using the binomial distribution. The null hypothesis states that the manufacturer is meeting its goal, while the alternative hypothesis states otherwise. By calculating the probability of observing 98 or more overfried chips in a random sample of 111,667 chips, we can determine if the manufacturer is meeting its goal.

Step-by-step explanation:

To determine if the manufacturer is meeting its goal for overfried chips, we can conduct a hypothesis test. The null hypothesis, denoted as H0, states that the manufacturer is meeting its goal of producing less than 1 overfried chip in every 1000 chips. The alternative hypothesis, denoted as H1, states that the manufacturer is not meeting its goal. The significance level, alpha (α), is given as 0.05.

We can use the binomial distribution to model the number of overfried chips. The expected number of overfried chips can be calculated by multiplying the sample size (111,667) by the probability of producing an overfried chip (0.001).

Using the binomial distribution, we can calculate the probability of observing 98 or more overfried chips in a random sample of 111,667 chips. If this probability is less than the significance level (α = 0.05), we reject the null hypothesis and conclude that the manufacturer is not meeting its goal.