Statistics project

This assignment requires stat crunch!!!! Please only inquire if you are familiar with this program. Will provide log in information for stat crunch to access data set. Will tip generously!!! Thanks!Rounding Rules: 
− In Section 1, all upper and lower class bounds should be integers. 
− In Section 2, do not round the five-number summaries. 
 − Round all other sample statistics in Section 2, as well as the confidence limits in Section
3, to one decimal place. 
− Round all p-values—one each in Sections 4 and 5—to three decimal places. 
− In Section 5, round all StatCrunch output (besides the p-values) to one decimal place.
− Add trailing zeroes to any rounded value as needed. 
− Do not simply paste screen shots of StatCrunch output into your report. 
− Warning: do not use the sample project as an example of how to round! The data set used in that
particular project is different from yours, so the values are all rounded differently! 
Required Content: Organize your report in five separate sections using the following numbers
and titles. The required elements for each section are as follows: 

Section 1 – Visual Data Assessment. For each variable of interest – Percent Time Asleep and
Longevity – create a grouped frequency histogram. For the Percent Time Asleep histogram,
use a lower limit of 0.0 and a class width of 10.0. For Longevity, use a lower limit of 10.0
and a class width of 10.0. Each histogram must include an informative title, along with
correct labels for both axes. For each histogram, include a paragraph that answers each of
the following questions: 
a. Is the histogram symmetric, left-skewed, right-skewed, or uniform? 
b. How many peaks does the histogram have, and in which class(es) are they located
(must include the correct lower and upper bounds for each class listed)? 
c. Does the histogram have any gaps between classes? If so, where are they? 

Section 2 – Descriptive Statistics. 
a. For each variable, find the mean, range, variance, standard deviation, and five-number summary. Display these numbers in a format that is easy to understand.
(Do not simply copy screencaps of the StatCrunch output!) 
b. Construct a regular boxplot for each variable. For each boxplot, include a brief
statement containing an assessment of whether the data appear to be symmetric,
left-skewed, right-skewed, or uniform. 
c. For each variable, construct a modified boxplot and use it to identify potential
outliers. If any exist, list them by value; if none exist, say so. 

 Section 3 – Confidence Intervals. Construct a 95% confidence interval for the mean μ of each
variable (two intervals total). You may use either algebraic or interval notation as shown in
the course notes. State the distribution you used for each interval (𝑡𝑡 or normal). 

Section 4 – Hypothesis Test. Using the p-value method, conduct a formal hypothesis test of
the claim that 𝜇𝜇, the mean longevity of fruit flies, is less than 57 days. Use 𝛼𝛼 = 0.01. Include
the following in your written summary of the results: 
a. Your null and alternate hypotheses in the proper format using standard notation. 
b. The type of distribution you used (𝑡𝑡 or normal). 
c. The p-value and its logical relationship to 𝛼𝛼 (≤ or >). 
d. Your decision regarding the null hypothesis: reject or fail to reject. 
e. A statement interpreting your decision: reject/fail to reject (or support/fail to
support) the original claim that the mean longevity of fruit flies is less than 57 days. 
Note: Section 4 only applies to Longevity. There is no hypothesis test related to Percent
Time Asleep. 

Section 5 – Correlation/Regression Analysis. 
a. Construct a linear regression model with Percent Time Asleep as the predictor and
Longevity as the response. State the equation in correct algebraic format as shown in
the course notes. 
b. Create a scatter plot of the data with a plot of the least squares line included.
(StatCrunch should have generated this plot when you calculated the model in 5a.)
The plot must include an informative title and correct labels for both axes. 
c. Use the coefficient of determination to identify the percentage of the variation in
Longevity explained by the variation in Percent Time Asleep. 
d. Identify all likely influential points (Cook’s Distance greater than 1.0). If any exist,
list them as ordered pairs in the form (Percent Time Asleep, Longevity). If none
exist, say so. 
e. Conduct a formal hypothesis test at 𝛼𝛼 = 0.05 to determine if there is sufficient
evidence of correlation between Percent Time Asleep and Longevity. Include the
following:
1) The p-value and its logical relationship to 𝛼𝛼 (≤ or >).
2) Your decision regarding the null hypothesis: reject or fail to reject.
3) A statement regarding the sufficiency of the evidence for a linear relationship
between Percent Time Asleep and Longevity. 
f. State whether the equation in 5a satisfies the following LINE criteria (assume the
residuals are independent):
Linear Relationship (L): Using the scatterplot with fitted line, determine if a linear
model is appropriate based on the model’s visual fit to the data.
Independent Residuals (I): Include a statement that the residuals are assumed to be
independent.
Normally-Distributed Residuals (N): Determine if the residuals fit a normal
distribution using a residual histogram and a Q-Q plot. (Do not use a boxplot.)
Verify your assessment by conducting a Shapiro-Wilk goodness-of-fit test for
normality on the model residuals. Use 𝛼𝛼 = 0.05. Report the p-value, its logical
relationship to 𝛼𝛼 (≤ or >), and your interpretation of the result.
Equal Variances of the Residuals (E): Assess the residuals for constant variance
using a plot of the residuals versus Percent Time Asleep. 
g. Using the results from 5e and 5f, clearly state whether the model you built in 5a
provides valid estimates of Longevity as a function of Percent Time Asleep. Justify
your claim. 
h. Provide a valid estimate of 𝑦𝑦𝑛𝑛𝑛𝑛𝑛𝑛, a new observation of Longevity for a fruit fly with
Percent Time Asleep = 20. Use either the regression model you constructed in 5a or
calculate the value using the Longevity data column by itself, whichever is
appropriate. 
 i. If you use the regression model from 5a to calculate the estimate in 5h, calculate a
95% prediction interval estimate of 𝑦𝑦𝑛𝑛𝑛𝑛𝑛𝑛. If the model in 5a is invalid, include a
statement that a prediction interval estimate is not applicable