Apple juice contains trace amounts of arsenic, measured in parts per billion (ppb). Over the past five years, I have been sampling apple juices and measuring their arsenic concentrations. You are being given a data set (the “Juice” sheet) containing the arsenic concentrations and the years in which I measured them. (You can assume that the experiment was conducted well, the sampling was done properly, etc.) a) Create a visualization that depicts the distribution of the concentration data, and describe that distribution. “Describe” goes beyond simply naming the shape! b) These data are stratified by year. Create an individual confidence interval about the sample mean for each year. (So, you’ll have 5 different intervals.) Is apple juice getting any more or less safe as time goes on? c) Each year, the generally accepted consensus was that the typical concentration is 2.25 ppb. Do we believe this? d) Why is the interval for 2021 so much tighter than the rest? e) Comment on whether any data values in this data set should be removed. Data Set in Excel Year Concentration 2019 1.49 2022 3.05 2020 2.53 2021 2.37 2019 3.49 2019 2.62 2023 2.8 2023 3.69 2020 3.04 2022 1.62 2021 2.11 2019 0.05 2023 3.31 2023 3.51 2019 2.66 2023 4.05 2023 1.36 2019 1.96 2019 1.12 2020 1.76 2019 1.62 2023 2.06 2019 1.17 2023 2.14 2021 0.46 2019 -0.5 2023 1.01 2022 1.66 2021 1.85 2020 2.3 2021 3.59 2020 1.56 2020 1.82 2019 1.34 2019 1.97 2023 2.46 2019 3.08 2019 2.87 2022 4.27 2022 2.52 2021 1.09 2019 0.33 2021 1.88 2021 2.52 2023 2.96 2022 1.35 2021 2.94 2022 2.6 2021 2.01 2019 1.58 2022 1.77 2022 3.25 2022 0.82 2022 3.65 2022 2.34 2021 1.67 2021 1.99 2020 0.7 2022 2.12 2021 2.36 2023 2.33 2023 1.46 2019 3.18 2021 2.92 2023 6 2023 8

Apple juice contains trace amounts of arsenic, measured in parts per billion (ppb). Over the past five years, I have been sampling apple juices and measuring their arsenic concentrations. You are being given a data set (the “Juice” sheet) containing the arsenic concentrations and the years in which I measured them. (You can assume that the experiment was conducted well, the sampling was done properly, etc.) a) Create a visualization that depicts the distribution of the concentration data, and describe that distribution. “Describe” goes beyond simply naming the shape! b) These data are stratified by year. Create an individual confidence interval about the sample mean for each year. (So, you’ll have 5 different intervals.) Is apple juice getting any more or less safe as time goes on? c) Each year, the generally accepted consensus was that the typical concentration is 2.25 ppb. Do we believe this? d) Why is the interval for 2021 so much tighter than the rest? e) Comment on whether any data values in this data set should be removed. Data Set in Excel Year Concentration 2019 1.49 2022 3.05 2020 2.53 2021 2.37 2019 3.49 2019 2.62 2023 2.8 2023 3.69 2020 3.04 2022 1.62 2021 2.11 2019 0.05 2023 3.31 2023 3.51 2019 2.66 2023 4.05 2023 1.36 2019 1.96 2019 1.12 2020 1.76 2019 1.62 2023 2.06 2019 1.17 2023 2.14 2021 0.46 2019 -0.5 2023 1.01 2022 1.66 2021 1.85 2020 2.3 2021 3.59 2020 1.56 2020 1.82 2019 1.34 2019 1.97 2023 2.46 2019 3.08 2019 2.87 2022 4.27 2022 2.52 2021 1.09 2019 0.33 2021 1.88 2021 2.52 2023 2.96 2022 1.35 2021 2.94 2022 2.6 2021 2.01 2019 1.58 2022 1.77 2022 3.25 2022 0.82 2022 3.65 2022 2.34 2021 1.67 2021 1.99 2020 0.7 2022 2.12 2021 2.36 2023 2.33 2023 1.46 2019 3.18 2021 2.92 2023 6 2023 8

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter4: Equations Of Linear Functions

Section4.5: Correlation And Causation

Problem 15PPS

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Question

I had bartleby Artificial Intelligence help me with parts (a), (b), (c), (d), and (e) on this Intro to Probability and Statistics homework problem. I am not sure if these answers are correct(see answers below). You can use Excel to help you complete this homework problem. Below the the homework problem, is a data set in Excel that will be used for this problem. Make sure the answers that you provide are long. Also, make sure your handwriting is neat and readable.

Answers from bartlbey Artificial Intelligence

Step 1

The objective of the question is to analyze a dataset of arsenic concentrations in apple juice over a period of five years. The analysis includes creating a visualization, calculating confidence intervals, testing a hypothesis, and identifying outliers.

Step 2

a) To create a visualization that depicts the distribution of the concentration data, we can use a histogram. The histogram will show the frequency of different concentration levels. The shape of the distribution can be described in terms of its skewness (whether it leans more to the left or right), kurtosis (how peaked or flat it is), and any noticeable peaks or valleys.

Step 3

b) To create an individual confidence interval about the sample mean for each year, we first calculate the mean and standard deviation for each year. Then, we use the t-distribution to calculate the confidence interval. The formula for a confidence interval is mean ± (t-value * standard deviation / sqrt(sample size)). If the confidence intervals for later years do not overlap with those for earlier years, we can conclude that the arsenic concentration is changing over time.

Step 4

c) To test the consensus that the typical concentration is 2.25 ppb, we can perform a one-sample t-test. The null hypothesis is that the mean concentration is 2.25 ppb. If the p-value is less than 0.05, we reject the null hypothesis and conclude that the mean concentration is not 2.25 ppb.

Step 5

d) The interval for 2021 is tighter than the rest because the standard deviation for that year is smaller. This means that the data points for 2021 are closer to the mean, resulting in a smaller confidence interval.

Step 6

e) To determine whether any data values should be removed, we can look for outliers. Outliers can be identified using the IQR method, where any value less than Q1 - 1.5*IQR or greater than Q3 + 1.5*IQR is considered an outlier. If any outliers are found, we need to investigate further to determine whether they are due to measurement errors or other anomalies.

Homework Problem

a) Create a visualization that depicts the distribution of the concentration
data, and describe that distribution. “Describe” goes beyond simply
naming the shape!

b) These data are stratified by year. Create an individual confidence interval
about the sample mean for each year. (So, you’ll have 5 different intervals.)
Is apple juice getting any more or less safe as time goes on?

c) Each year, the generally accepted consensus was that the typical concentration
is 2.25 ppb. Do we believe this?

d) Why is the interval for 2021 so much tighter than the rest?

e) Comment on whether any data values in this data set should be removed.

Data Set in Excel

Year Concentration
2019 1.49
2022 3.05
2020 2.53
2021 2.37
2019 3.49
2019 2.62
2023 2.8
2023 3.69
2020 3.04
2022 1.62
2021 2.11
2019 0.05
2023 3.31
2023 3.51
2019 2.66
2023 4.05
2023 1.36
2019 1.96
2019 1.12
2020 1.76
2019 1.62
2023 2.06
2019 1.17
2023 2.14
2021 0.46
2019 -0.5
2023 1.01
2022 1.66
2021 1.85
2020 2.3
2021 3.59
2020 1.56
2020 1.82
2019 1.34
2019 1.97
2023 2.46
2019 3.08
2019 2.87
2022 4.27
2022 2.52
2021 1.09
2019 0.33
2021 1.88
2021 2.52
2023 2.96
2022 1.35
2021 2.94
2022 2.6
2021 2.01
2019 1.58
2022 1.77
2022 3.25
2022 0.82
2022 3.65
2022 2.34
2021 1.67
2021 1.99
2020 0.7
2022 2.12
2021 2.36
2023 2.33
2023 1.46
2019 3.18
2021 2.92
2023 6
2023 8

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