I have problem understading and doing this AP prolem. Please help me explain it clearly so that I could understand it.
Problem: Since Hill Valley High School eliminated the use of bells between classes teachers have noticed that more students seem to be arriving to class a few minutes late. One teacher decided to collect data to determine wheather the students' and teachers' watches are displaying the correct time. At exactly 12:00 noon, the teacher asked 9 randomly selected students and 9 randomly selected teachers to record the times on their watches to the nearest half minute. The ordered data showing minutes after 12:00 as positive values and minutes before 12:00 as negative values are shown in the table below.
Students -.5 -3.0 -.5 0 0 .5 .5 1.5 5.0
Teachers -2.0 -1.5 -1.5 -1.0 -1.0 -.5 0 0 .5
A) construct parallel boxplots using these data
B) Based on the boxplots in part (a), which of the two groups, students or teachers, tends to have watch times that are closer to the true time? explain you choice
C) The teacher wants to know wheather individual student's wathces tend to be set correctly/ She proposes to test H nought: mean equal o versus H alternative: mean cannot equal 0, where the mean represents the mean amount by which all student watches differ from the correct time. Is this an sppropriate pair of hypotheses to test to answer the teacher's question? Explain why or why not. Do not carry out the test.
what are boxplots?
there almost like intugures...i think ....dont listen to me!!!
Boxplots, also known as box and whisker plots, are visual representations of data that display the distribution, spread, and skewness of a dataset. They are useful for summarizing large amounts of data and providing a quick overview of key characteristics such as central tendency, dispersion, and outliers.
To construct a boxplot, you need the minimum value, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum value of the dataset. The boxplot consists of several components:
1. The box: It represents the middle 50% of the data, stretching from Q1 to Q3. The line inside the box represents the median.
2. The whiskers: These are lines extending from the box to the minimum and maximum values, excluding outliers. They show the spread of the data.
3. Outliers: Any data values that fall outside the whiskers are considered outliers and are represented as individual points.
Now let's look at how to construct parallel boxplots for the given data in part (a) of the problem.
First, arrange the data in ascending order:
Students: -3.0, -.5, -.5, 0, 0, .5, .5, 1.5, 5.0
Teachers: -2.0, -1.5, -1.5, -1.0, -1.0, -.5, 0, 0, .5
Next, calculate the necessary values:
- Minimum: The smallest value in each dataset (-3.0 for students and -2.0 for teachers).
- Lower Quartile (Q1): The median of the lower half of the data (between the minimum and the median of the entire dataset).
- Median (Q2): The middle value of the dataset.
- Upper Quartile (Q3): The median of the upper half of the data (between the median and the maximum of the entire dataset).
- Maximum: The largest value in each dataset (5.0 for students and 0.5 for teachers).
Finally, construct the boxplots:
_________________
Students: -3.0 | | +5.0
|_______|
Teachers: -2.0 | | +0.5
|_______|
In the above boxplots, the horizontal line inside the box represents the median, while the box represents the middle 50% of the data. The whiskers extend from the box to the minimum and maximum values.
Now, let's move on to part (b) of the problem and determine which group, students or teachers, tends to have watch times closer to the true time based on the boxplots.
Looking at the boxplots, we can see that the box for the students is shorter, indicating less variability in watch times compared to the teachers. Additionally, the median for the students is closer to the zero mark (representing the correct time) compared to the teachers. Therefore, we can conclude that students tend to have watch times that are closer to the true time, based on the boxplots.
Moving on to part (c) of the problem, let's analyze whether the proposed pair of hypotheses is appropriate to test for determining whether individual student watches tend to be set correctly.
The hypotheses proposed are:
H0: mean = 0
Ha: mean ≠ 0
In these hypotheses, the mean represents the average difference between individual student watches and the correct time. The teacher wants to investigate if there is a significant difference between the individual watches and the correct time.
This is an appropriate pair of hypotheses. The null hypothesis (H0) assumes that the mean difference between the watches and the correct time is zero, indicating that the watches are set correctly. The alternative hypothesis (Ha) assumes that the mean difference between the watches and the correct time is not zero, indicating that there is a significant difference.
To determine whether the null hypothesis is supported or rejected, a statistical test (such as a t-test or a confidence interval) would need to be performed using the data. However, carrying out the test is not necessary for answering this part of the problem.
I hope this explanation clarifies the problem for you. If you have any further questions, feel free to ask!