A scientist studying consumption of sugar, its effects, and links to things like Diabetes and weight gain is performing a study on sugar intake in things like coffee and tea. She and her team are interested in the number of servings and if in fact each serving is providing the expected quantity that the person consuming the beverage believes.
The team has been studying the various distributions from things like sugar packets and is now looking at servings of sugar from teaspoons.
If 4.2 grams of sugar is equal to a teaspoon (which is considered one serving), the team is studying a particular restaurant that provides teaspoons to customers during breakfast and allows them to add sugar to their beverages.
The team collects data from two (2) different types of spoons (both considered teaspoons) which have differing shapes to identify if there is a difference in the variation between the servings per teaspoon a customer puts into their cup or glass.
The results of randomly selected customers are shown in table 1 below.
Table 1: Weight in Grams of Sugar per serving
Spoon Type 1 Spoon Type 2
4.23 4.14
4.01 4.17
4.29 4.15
4.35 4.26
4.06 4.35
4.05 4.2
4.15 4.05
3.75 4.25
4.19 4.32
4.41 4.11
4.52 4.21
4.37 4.25
4.21 4.31
4.05
4.02
4.12
4.28
4.14
At the 10% level of significance, is there a difference between the serving variations when customers used spoon type 1 as compared to spoon type 2?