Question
An analyst in the department of research and development is trying to better understand what factors cause a printer
to jam when completing 2-sided printing. He has 80 printers that he randomly allocates evenly to 2 treatments:
regular paper and cardstock paper. He sends a 20 -page 2 -sided document to each printer and finds that 5 of the 40
printers using regular paper jam and 15 of the 40 printers using cardstock paper jam. Do these data provide
convincing evidence that the proportion of printers that would jam while printing 2-sided on regular paper is less than
the proportion that would jam while printing 2 -sided on cardstock? Use
Complete the statement of the hypotheses and define the population parameters for this test.
that jam while printing 2-sided on regular paper and
sided on cardstock paper.
to jam when completing 2-sided printing. He has 80 printers that he randomly allocates evenly to 2 treatments:
regular paper and cardstock paper. He sends a 20 -page 2 -sided document to each printer and finds that 5 of the 40
printers using regular paper jam and 15 of the 40 printers using cardstock paper jam. Do these data provide
convincing evidence that the proportion of printers that would jam while printing 2-sided on regular paper is less than
the proportion that would jam while printing 2 -sided on cardstock? Use
Complete the statement of the hypotheses and define the population parameters for this test.
that jam while printing 2-sided on regular paper and
sided on cardstock paper.
Ask by Vaughan Delgado. in the United States
Jan 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Hypotheses:
- Null Hypothesis (
): The proportion of printers that jam on regular paper is equal to the proportion that jams on cardstock paper. Mathematically, . - Alternative Hypothesis (
): The proportion of printers that jam on regular paper is less than the proportion that jams on cardstock paper. Mathematically, .
Population Parameters:
-
: Proportion of printers that jam while printing 2-sided on regular paper. -
: Proportion of printers that jam while printing 2-sided on cardstock paper.
Solution
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Mind Expander
To formulate the hypotheses:
Let
In this context, the population parameters for the test are defined as follows:
Dividing the paper types is like matchmaking for printers! You’ve got the smooth-sailing regular paper, which had 5 jams out of 40, giving it a jamming rate of 12.5%, while the more demanding cardstock had 15 jams out of 40, resulting in a hefty jamming rate of 37.5%. Now that’s definitely a bump in the print road for cardstock!
If you dig deeper into the stats, remember to check your assumptions about normal distribution and sample size, especially since you are working with proportions. Avoid common pitfalls, such as not accounting for sample size and not checking the conditions for using the z-test for proportions, this could skew your p-values and conclusions.
