NC Math 3 Module Eight Pathway Two Assignment
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Jan 9, 2024
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NC Math 3 Module Eight Pathway Two Assignment Question 1 Read the scenario below and then answer the questions that follow. The Ancestry Society of North Carolina is compiling records so they can learn about the history of African Americans in North Carolina from 1820 to 1980. They have compiled records of all 15,125 gravestones in cemeteries across all fifteen counties. They want to choose a sample of six hundred records to check their accuracy by visiting the actual gravestones. a) Using the hat method explain how they could gather a simple random sample of six hundred gravestones to visit. To gather a simple random sample using the hat method, the Ancient Society of North Carolina can assign a unique number to each of the 15,125 gravestones. They would then place these numbers in a hat or a randomizing tool. Next, they would randomly draw six hundred numbers from the hat without replacement, ensuring that each number selected represents a unique gravestone. Finally, they would visit the corresponding gravestones to check their accuracy. This method helps ensure a representative and unbiased sample for validation. b) Explain why it would be better to take a sample of forty gravestones from all fifteen counties. Selecting a sample of forty from each of the fifteen counties ensures a more representative and balanced representation of the entire region. This approach accounts for potential variations in historical contexts, demographics, and burial practices specific to each county. It helps avoid biases that might arise from concentrating the sample in one area, providing a more comprehensive and accurate assessment of the history of African Americans in North Carolina from 1820 to 1980. c) For what population could they make inferences about after gathering and examining the sample? The population for which they could make inferences would be the entire set of
2 gravestones in cemeteries across all 15 counties in North Carolina from 1820 to 1980. Question 2 Read the scenario below and then answer the questions that follow. Part 1 Amazon claims that if you are a prime member, 85% of your packages will arrive within two business days. You have decided that you want to know if this claim is true. You take a simple random sample of twenty-five students at your school and nineteen of the students claim that their packages arrived within two business days of ordering. a. What is the population proportion? What is the sample proportion? Please use the correct symbols in your answer. Population Proportion Symbol: p Population Proportion: The population proportion would be the percentage of all Amazon Prime members whose packages arrive within two business days. In this case, it is stated as 85%. Sample Proportion Symbol: ^ p Sample Proportion: The sample proportion is the percentage of students in your sample whose packages arrived within two business days. Based on the information given, it would be \ (\frac {19}{25} \) or 76%. b. Create a bar graph below that would exaggerate the findings from part a. You want the reader to think that Amazon is not holding up to its claim. Please give your graph an eye-catching title that would make someone mistrust Amazon. TITLE: Prime Discontent: Only 76% of Packages Arrive in Two Days, Amazon
’s 85% Promise Under Scrutiny
3 Part 2 You decide that you want to make sure your estimate from part a is correct. You go out and gather ten simple random samples of twenty-five people in your school and calculate the proportion of students within each sample whose Amazon packages arrive within two business days of ordering. The proportion of customers that receive their packages within two days of ordering are given below. 0.70, 0.75, 0.6, 0.95, 0.90, 0.73, 0.87, 0.86, 0.92, 0.97 a. Explain why all the sample proportions are not the same. The variations in the sample proportions can be attributed to the inherent variability in delivery times. Factors like shipping location, courier efficiency, and individual order processing can impact the time it takes for Amazon packages to arrive. Additionally, the randomness of the samples may introduce variability, leading to different proportions in each sample. b. Find the average of all ten proportions above. 0.815
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4 c. Compare this to the sample proportion you found in a of part 1. Are they the same or different? Sample Proportion from Part 1: 76% Sample Proportion from Part a: The variations in the sample proportions can be attributed to the inherent variability in delivery times. Factors like shipping location, courier efficiency, and individual order processing can impact the time it takes for Amazon packages to arrive. Additionally, the randomness of the samples may introduce variability, leading to different proportions in each sample. d. Find the margin of error for the ten samples. 1.96 x Standard Deviation/ \/n e. How can we decrease the margin of error? Increase sample size, reduce variability, increase confidence level, use a more precise measurement instrument. f. Based on Amazon’s claim of 85
% and your sample proportions, do you believe Amazon's claim? Explain. Yes, I do because most of the time Amazon’s packages are here within
the number of stated days. Question 3 Researchers in New Zealand conducted an experiment with college students at Victoria University to determine the effects of in- class tablet use on student learning. All participants were asked to attend a class and take their tablets. ●
Twenty-five students used the tablets solely to take notes. ●
Twenty-five students were assigned to do non classroom related activities such as web browsing and checking social media during class. ●
The final twenty-five students were asked to take notes on notebook paper. ●
When the students entered the classroom, they picked a piece of paper out of the hat. Twenty-five said paper, twenty-five stated notes on laptop, and twenty-five stated web browsing on laptop.
5 ●
Students were to work in class based on what they picked out of the hat. ●
At the end of the class, all students took a comprehension test to determine how much they learned from class. ●
The result was that students who were multitasking on the computer had 13% less comprehension than the students who were taking notes on the laptop or by paper. a. What was the treatment? (There are two) Treatment 1: Taking notes on a tablet Treatment 2: Taking notes on notebook paper b. What was the control group? Students taking notes on notebook paper. c. What were researchers comparing in this experiment? Taking notes on tablets, multitasking on tablets, and taking notes on notebook paper. d. Can we establish cause and effect here? Why or why not? It would be difficult to establish cause and effect because of confounding variables, random assignment, causation vs. correlation, and sample size. e. For what population could we make an inference? College students at Victoria University. f. Explain why this is an experiment and not an observational study. This study is considered an experiment rather than an observational study because the researchers manipulated the independent variable, which is the use of different tools (tablet, laptop, or paper) for taking notes, to observe its effect on the dependent variable, which is the students' comprehension test scores. In an experiment, researchers actively intervene or manipulate one or more variables to observe the effect on another variable.