Question

Please help!!

you will thoroughly analyze a set of data. First you are to describe the data so that the reader can
place it in context, then do each of the following. Your analysis will include all the items mentioned
below, making sure you explain yourself at each step. Graphs, calculations, and numbers without
comment are not allowed. Put this all nicely together as one item, ordering items close to how they are
given below.
Use the data set on the other side of the page. Make a histogram and analyze it using terms learned in
class. Present a 5 number summary and modified box plot. Are there any outliers? Report the mean
and standard deviation. (DO NOT discard outliers) The mean was important in this experiment.
Calculate a 95% confidence interval for the true mean. Explain what this means. Compare these (5
number summary and mean/standard deviation). Are the mean and standard deviation valid for this
set of data? Justify your answer. Some of the above (and what follows below) makes no sense if the
data is not approximately normal. Explain what this means. Is this data close to normally distributed?
Justify your answer. Regardless of your conclusion, for the next part assume the data is approximately
normal. \
The data is listed in the order it was recorded (down first, then across). Do a time plot. Analyze this plot,
paying special attention to new information gained beyond what we did above. Cut the data in half
(first three columns vs. last three columns) and do a back to back stem plot. Analyze this. Does this
further amplify what the time plot showed? Calculate the mean of the second half of the data. Using
the mean and standard deviation of the whole data set (found above) as the population mean and
standard deviation, test the significance that the mean of the second half is different than the mean of
the total using a = 0.05. Make sure to clearly identify the null and alternative hypothesis. Explain what
this test is attempting to show. Report the p-value for the test and explain what that means. Accept or
reject the null hypothesis, and justify your decision (based on the pvalue).

Answer 1

To thoroughly analyze the given data set, we will follow the steps provided:

1. Describing the data:
- The data set is listed in a specific order, with the values recorded vertically and then horizontally.
- It is important to note that the context or nature of the data is not specified.

2. Creating a histogram:
- We will construct a histogram using the data set.
- The histogram will provide a visual representation of the distribution of the data.

3. Analyzing the histogram:
- We will use terms learned in class to analyze the histogram, such as shape (symmetrical, skewed, etc.), central tendency, and spread.
- This analysis will help us understand the characteristics of the data distribution.

4. Presenting a 5-number summary and modified box plot:
- We will calculate the five-number summary (minimum, first quartile, median, third quartile, maximum) for the data set.
- Using this summary, we will construct a modified box plot to visualize the distribution and identify any potential outliers.

5. Identifying outliers:
- We will examine the modified box plot to identify any outliers in the data set.
- Outliers are values that significantly deviate from the rest of the data and may have an impact on the mean and standard deviation.

6. Calculating the mean and standard deviation:
- We will calculate the mean and standard deviation for the entire data set.
- The mean represents the average value of the data, while the standard deviation measures the spread or variability around the mean.

7. Interpreting the 95% confidence interval for the true mean:
- We will calculate a 95% confidence interval for the true mean of the data.
- This interval will provide a range within which we are 95% confident that the true population mean lies.

8. Comparing the 5-number summary and mean/standard deviation:
- We will compare the characteristics of the data set provided by the 5-number summary and the mean/standard deviation.
- This will help us determine if the mean and standard deviation are valid measures for this particular data set.

9. Assessing normality of the data:
- We will discuss the concept of data being approximately normal and its implications.
- We will examine the histogram and other visualizations to determine if the data appears to follow a normal distribution.

10. Time plot analysis:
- We will create a time plot using the data set, considering the order in which the data was recorded.
- The time plot will allow us to observe any trends or patterns in the data over time.

11. Analyzing the time plot:
- We will analyze the time plot, paying attention to any new information gained beyond the previous steps.
- This analysis will help us understand any temporal patterns or changes in the data.

12. Conducting a back-to-back stem plot:
- We will divide the data into two halves: the first three columns and the last three columns.
- Using a back-to-back stem plot, we will compare the distributions of the two halves and identify any differences.

13. Mean of the second half of the data:
- We will calculate the mean of the second half of the data set.
- This will help us compare the mean of the second half to the overall mean of the entire data set.

14. Testing the significance of the mean of the second half:
- Using the mean and standard deviation of the entire data set as the population parameters, we will conduct a hypothesis test.
- The null hypothesis will state that the mean of the second half is equal to the mean of the total, while the alternative hypothesis will suggest they are different.

15. Explaining the hypothesis test: