An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar. This new product is expected to increase profits substantially because they create the 50% less sugar product by replacing 50% of the juice with water while selling it for the same price. An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%.

He selects a random sample of 500 containers of orange juice and determined the percentage of each that is water. He plans to conduct a significance test at the a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50. What is the probability that the inspector makes a Type I error?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar.

An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%.

He plans to conduct a significance test at a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50.

Type I error is referred to as false positives and it means that when a statistically significant difference is validated by the researcher even though the results aren't statistically significant.

Type I error is when one rejects the null hypothesis even though it's true. In this case, the inspector rejects the hypothesis that the proportion of water that is contained in the product is 0.5.

The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.

Learn more about probability here;

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