Probability & Statistics Honors

Unit Test #5

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How much vitamin C does orange juice contain? The quality control manager at a processing plant selects every 100th bottle that is produced and checks the vitamin C content.

Use this information for the first three questions.



What is the population in this scenario?


All bottles of orange juice (everywhere).



To what group can the results of this study be generalized?


All bottles of orange juice from this plant



What sampling method has been described in this scenario?


Systematic random sampling



Researchers invited university students to take part in an experiment. While the students watched a video, a plate of brownies was offered to each student. The size and number of brownies were deliberately controlled (and made different) for each student, and the researchers measured the total weight of brownies that were eaten.

Is this an example of an observational study or an experiment? Why?


This is an experiment, since something was changed (the size and number of brownies offered).



To fund a program to buy iPads for elementary students, a 5% property tax increase is proposed. A local “golden oldies” radio station asks listeners to call in and voice their support or opposition to the increase.

What type of bias is present in this sampling technique?


Voluntary response


Researchers asked participants in a study to have one of four snacks before a meal. The amount served during the snack and the meal was carefully controlled, and the researchers measured how much (mass) of the meal was eaten in each case.

Use this information for all questions on this page.



What are the experimental units in this experiment?


The participants (people)



What is/are the explanatory variable/s in this experiment?


The type of snack offered



How many treatments are there in this experiment?





What is the response variable in this experiment?


How much (mass) of the meal that was eaten



Is this experiment double blind?


No. The participants should be able to identify the different types of snacks.



Why was it important for the researchers to randomly assign the experimental units to each of the treatments?


To deal with unknown variables that might have an effect on how much each person ate.



A fast food franchise is test marketing 3 new menu items. To find out if they the same popularity, 18 restaurants are randomly chosen for participation in the study. 6 of the restaurants are randomly chosen to test market the first new menu item, another 6 for the second menu item, and the remaining 6 for the last menu item.

What type of experimental design is being described?


Completely randomized



Researchers want to know how a new diet affects weight loss compared to a standard diet. They recruit 100 subjects, then group the subjects into 50 pairs based on their age and gender. Then, within each pair, one subject will randomly be assigned to follow the new diet for 30 days and the other subject will be assigned to follow the standard diet for 30 days. At the end of the 30 days, researchers will measure the total weight loss for each subject.

What type of experimental design is being described?


Matched pairs


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