Question

Use the following information to answer the next three exercises: A study is done to determine which of two soft drinks has more sugar. There are 13 cans of Beverage A in a sample and six cans of Beverage B. The mean amount of sugar in Beverage A is 36 grams with a standard deviation of 0.6 grams. The mean amount of sugar in Beverage B is 38 grams with a standard deviation of 0.8 grams. The researchers believe that Beverage B has more sugar than Beverage A, on average. Both populations have normal distributions.

Are standard deviations known or unknown?

Short answer

The population standard deviations are unknown in both cases.

Step-by-step solution

Given information

A study is being conducted to see which of two soft drinks contains the most sugar. A sample contains 13 cans of Beverage A and six cans of Beverage B. Beverage A contains 36 grammes of sugar on average, with a standard variation of 0.6 grammes. Beverage B has 38 grammes of sugar on average, with a standard variation of 0.8 grammes. Beverage B, on average, has more sugar than Beverage A, according to the experts. The distributions of both populations are normal.

Is it possible to know both population standard deviations?

The sample standard deviations for both beverages' sugar content are known. The population standard deviations, however, are unknown.