# Math 138 - A Comprehensive Statistical Project - Using StatCrunch

A Comprehensive Statistical Project (Before CH 25) Using StatCrunch

Total = 45 points

Instructions for completing Project Answers to the project must:
1. Be submitted online, using the Assignment or Module Tools by the due date.
2. Include at least your first initial and last name at the beginning of the first page-- to avoid losing points.
______________BEGINNING OF PROJECT QUESTIONS/TASKS_____________

Using StatCrunch, load the data file: CPS Wage Data From 1985. Note: The same project questions would apply even if the data were from 2005 or later, if available.
Hint: Data > Load Data > From Sample Data > Stat Crunch > Highlight only CPS Wage Data From 1985
• Before opening the data file, click on “info” and make a note of the codes for “race” and “sex”.
• After becoming familiar with the codes, click on “close”; click on “Okay” (to load the data) into StatCrunch.

Question (Q1): Classify each of the following variables as either categorical or quantitative with units and briefly explain your classification (to receive full credit).
[1]1a. Education

[1]1b. Marr

Q2: Construct and analyze the data using a contingency table:
• For the 534 persons in the CPS, construct a contingency table of counts with “Race” = row variable and “Sex” = column variable;
• Hint: Stat > Table > Contingency > With data > Select row and column variables > next > Uncheck Chi-Square > calculate.
[2] Include this table with your project submittal by (within StatCrunch), click option > copy, then paste in the document that you plan to submit. (First of 3 attachments);
• Use this contingency table to answers (Q)2a – (Q)2c. Write your answer as a percent to one decimal place.
[2] 2a. Determine the percentage of (Other and Male) from the 534 persons.

[2] 2b. Determine the percentage of female, given the Hispanics is the only Race being considered.

Problem 2 continued:
[2] 2c. [Show your work] Determine the percentage of (female or White) from the 534 persons.

Q3: Construct and analyze the data using boxplots

• For the 534 persons in the CPS, construct boxplots by:
Hint: Graphics > Boxplot > select Experience (work) > Group by “Sex” > check (default)-plot groups for each column > next > check both: use fences to identify outliers and draw boxes horizontally > next > create graph

Hint(This may also help): Stat > Summary Stats > Columns > Experience (Work in years) > Group by “Sex” > Accept default table groups for each column > Next > Accept the default statistics (highlighted) > calculate

[2] Include the boxplots on one pair of axes with your project submittal by(within StatCrunch), click option > copy, then paste in the document that you plan to submit. (Second of 3 attachments);
• Use these boxplots to answer (Q)3a – (Q)3e.

[2] 3a. Which measure of center best describes the “female” data for work experience? Explain your answer. Find the value of this statistic to one decimal place, if applicable.

[2] 3b. Which measure of spread best describes the “female” data for work experience? Explain your answer. Find the value of this statistic to one decimal place, if applicable.

[2] 3c. . Calculate the upper and lower fences for the female data, then indicate what values would be considered as outliers

[2] 3e. Which “sex” has more variation/spread? Explain your answer.

Q4: Construct and analyze the data using histograms

[2] 4a. Use the histogram above. SHOW YOUR WORK] What percentage of the MALES has more than 10 years of education? Write your final answer as a percent to one decimal place.

Q5: Applying the concepts of the Normal Distribution and the Sampling Distribution To The Data

For the 534 persons, assume the Normal model applies.
[2] 5a. . (Show your work by indicating the feature of the calculator used).What percent of the ages is less than 41years (to two decimal places)? For your benefit, make a sketch. (Write your final answer as a percent to one decimal place.
Hint(This may also help): Stat > Summary Stats > Columns > Experience (Work in years) > Group by “Sex” > Accept default table groups for each column > Next > Accept the default statistics (highlighted) > calculate

[2] 5b. For this problem (5b) only, PRETEND that the data for all of the 534 persons are not available to you-just the data for a sample of 100 persons selected from the 534 persons. Assume that the mean age for this sample was 37 years, with a standard deviation of 10. What percent of the mean ages would be greater than 38 years (to two decimal places)? (Show your work by indicating the feature of the calculator used).]

Q6: Analyzing The Data Using Linear Regression

For the grouped by “Sex” variable, create a scatterplot with a fitted line plot by:
Hint: Stat > Regression > Simple Linear > x variable = Education > y variable = Wages > Group by = Sex > next, next,… > Check “Plot Fitted Line > ..Click “next”> calculate. Click “next” at the top of page to see the fitted line plots for males and females. Note the codes given for “sex” on the plots. Use the linear regression to answer (Q)6a – (Q)6d).
[2] Attached this fitted line plot to your submittal by (within StatCrunch), click option > copy, then paste in the document that you plan to submit. (Attachment 3/3)

[2] 6a. For the “female” data, what is the value for the correlation coefficient (to two decimal places)? Does this value indicate a “strong” linear relationship between education and wages regarding females?

[2] 6b. Assume “r” is reasonable enough; therefore continue to answer the questions which follow: What is the linear model, in context, for the “females”. Write values to three decimal places.)

[2] 6c. (Show your work). If one the points was (14, 14.29), what is the predicted hourly wage for females (to two decimal places)?

[2] 6d. (Show your work). Determine the residual (see 6c) and indicate how well the linear model is predicting wages for “females”. (Write answer to two decimal places, to include the unit of measurement).

Q7: Analyzing The Data Using Confidence Intervals and Test of Hypotheses

For (Q)7a – (Q)7e: Assume that the data consist of a random sample of 534 persons from the CPS.

Problem Situation: The supervisor in charge of the CPS hypothesized that the mean age for the 534 persons would be 37.5 years of age. Test whether there is really a significant difference between the hypothesized mean age and the mean age from the sample. Use a level of significance of 0.05.

[1] 7a: What statistical test would you use for this problem situation?

Problem 7 continued:
[2] 7b. State your Null and Alternative hypotheses using English or standard statistical notation.
.

[2] 7c. State the value of the sample mean, the test statistics and the p-value for this problem (to three decimal places).
Note: p-value with at least 6 leading zeros will be considered as zero for an answer.

[2] 7d Write a conclusion regarding the null hypothesis. Be sure to include the p-value determined in 7c in your conclusion.

[2] 7e Write a 95% confidence interval (to two decimal places) using the sample mean and interpret this interval using standard statistical language. Does the 95% confidence interval help to verify your conclusion stated in 7d? Underline “Yes” or “No”, and then explain your answer.

_________________________ END-OF PROJECT_____________________________

Solutions got an A+ grade.

Samples Solutions for Question 3a and 3b are as follows:

3a. Which measure of center best describes the “male” data for work experience? Explain your answer. Find the value of this statistic to one decimal place, if applicable.
The male data is a bit skewed with more values being on the lower half of experience yet the mean being higher because of several outliers. Because of this we would prefer to represent the center using the median. Median=14

3b. Which measure of spread best describes the “female” data for work experience? Explain your answer. Find the value of this statistic to one decimal place, if applicable.
Again we see that the female data is slightly skewed because of a few larger values. The mean is almost points greater than the median so we would choose the median for a better representation of the data. Median=16

For the full solutions please purchase the solutions package.

Other Details about the Project/Assignment
Subjects: Statistics
Topic: Math 138 Project on Wage Data
Level: University / College
Tags:

### boxplots, statcrunch, advanced statistics

Price\$3.95

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 Frederick Burke Member Since: March 2003 Customer Rating: 94.7% Projects Completed: 795 Total Earnings: *Private* +1 Ratings from clients: 115
Project Details
Subjects: Statistics
Topic: Math 138 Project on Wage Data
Level: University / College
Tags:

## boxplots, statcrunch, advanced statistics

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