For this Final project, you will be analyzing data that was collected from the survey that I sent to you all during the first couple weeks of class! I hope you have fun learning a little more about your classmates in this Final Project.:) This dataset contains information from 178 students (98 students in STA 2023 and 80 students in MAC 1105).
NOTE: You DO NOT need to work with the actual data set for this. I have included all of the relevant summary statistics in the statements of the problems.
- Complete the assignment either on paper or on the computer.
- Make sure to answer all questions.
- Please try to include any sketches and work on the worksheet. If you are not able to, however, you may submit them as a separate document. (It's just a little easier to grade when it's all in one document.)
- If you do not have access to a printer, you can hand write your asnwers on a separate sheet and upload a picture.
- Upload completed worksheet to this assignment in Canvas.
If you have any questions, don't hesitate to ask!
NOTES/HINTS:
- The degrees of freedom for these problems is large, you may need to use StatCrunch or an online calculator to find the critical values for the t-distribution:
please follow the template attached
Name: _____________________________________________
1. Dr. H was interested in looking at how many siblings her students have. She used the data from the Class Survey to construct the following modified boxplot. Use this display to answer the following questions about the variable “Siblings”.
a. (1 pt) The overall shape of this distribution is: (circle one) LEFT-SKEWED SYMMETRIC RIGHT-SKEWED
b. (1 pt) Which values are potential outliers? ______________________________________
c. (2 pts) The middle 50% of the values lie between ________________ and _______________
2. Dr. H knows that many of her students juggle a lot outside of her class! She was particularly interested in learning more about how much her STA 2023 students work. The Class Survey data contained responses for 98 students in her STA 2023 courses. For the purposes of this assignment, assume this was a random sample. From this random sample, the mean hours worked was 22.9 with a standard deviation of 18.1.
Find a 90% confidence interval for the average number of hours worked by Dr. H’s students. (Round to two decimal places.) NOTE: Please show work (or explain how you used technology) to earn full credit.
a. (2 pts) What type of confidence interval should you use? Circle one and explain your answer below.
interval OR interval
b. (2 pts) Confidence Interval: __________________________
NOTE: SHOW WORK (or how you used technology) TO EARN FULL POINTS)
c. (2 pts) Write a statement to interpret your results.
3. Dr.H’s has been thinking about creating a Time Travel machine and is trying to figure out if she should program it to go to the Past or to the Future first. She claims that the true proportion of her students who would prefer to travel to the future is less than 50%. From the data collected in the Class Survey, she found that 82 of the 178 students surveyed preferred to travel to the future. At , can you support Dr.H’s claim?
a. (2 pts) Write out the hypothesis statements below and identify the parameter of interest.
Ho: _________________________ Parameter of Interest: true proportion of Dr. H’s students who
would prefer to travel to the future.
Ha: _________________________
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b. (1 pt) Which hypothesis represents the claim? Circle one: Null Hypothesis (H0) or Alternative Hypothesis (Ha) |
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c. (1 pt) Explain what type of hypothesis testing you will perform and verify that the conditions are met. |
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d. Test this hypothesis. (SHOW WORK TO EARN FULL CREDIT!) (2 pts) Clearly label a sketch with appropriate shading. Also, identify the Critical Value(s) and Test Statistic. (1 pt) Critical Value(s): _____________ (1 pt) Test Statistic: _____________ (2 pts) Would you reject or fail to reject the null hypothesis? Circle one: Reject H0 or Fail to Reject H0 Explain your choice: |
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e. (2 pts) Write a conclusion in the context of this problem. |
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FUTURE |
PAST |
4. Dr.H’s is interested in learning more about her students and wants to compare the average age of students of these students. She claims that there is no difference in the average age of students who chose to travel to the future and those who chose to travel to the past. She used the data collected in the Class Survey to compute summary statistics for each course. These values are displayed in the table. Assume that these samples were random and that the population variances are NOT equal. At , is there enough evidence to reject Dr. Pridemore’s claim?
a. (2 pts) Write out the hypothesis statements below and identify the parameters of interest.
Ho: ________________ Parameters of Interest: true average age of students who want to travel to the future
Ha: ________________ true average age of students who want to travel to the past
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b. (1 pt) Which hypothesis represents the claim? Circle one: Null Hypothesis (H0) or Alternative Hypothesis (Ha) |
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c. (1 pt) Explain what type of hypothesis testing you will perform and verify that the conditions are met. |
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d. Test this hypothesis. (SHOW WORK TO EARN FULL CREDIT!) (2 pts) Clearly label a sketch with appropriate shading. Also, identify the Critical Value(s) and Test Statistic. (1 pt) Critical Value(s): _____________ (1 pt) Test Statistic: _____________ (2 pts) Would you reject or fail to reject the null hypothesis? Circle one: Reject H0 or Fail to Reject H0 Explain your choice: |
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e. (2 pts) Write a conclusion in the context of this problem. |
5. Dr.H’s read the following online article Picking Random Numbers: It's More Complicated Than You Think and was interested to see how her classes would do at picking random numbers. In the Class Survey, Dr. H asked her students to pick a random number between 1 and 10. In the dataset, the variable “Random10” represents the number that a student chose. Dr.H’s created the bar graph and frequency distribution for the numbers that students selected.
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Frequency |
Relative Frequency |
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1 |
3 |
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2 |
16 |
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3 |
20 |
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4 |
19 |
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5 |
10 |
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6 |
23 |
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7 |
59 |
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8 |
20 |
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9 |
7 |
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10 |
1 |
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Total |
a. (2 pts) Fill in the relative frequency column in the table. (Round to THREE decimal places.)
b. (4 pts) Read over the article Picking Random Numbers: It's More Complicated Than You Think. After reading over the article and looking at the bar graph and table, above, does it appear that the students in Dr.H’s classes were able to choose numbers randomly? Why or why not? Comment on anything interesting you learned from the article or interesting features that stand out from the displays above.
6. Let’s take a closer look at the data from the Random Numbers question with a Chi-Square Goodness-of-Fit test. At , can you support the claim that the distribution of numbers in this “Random Numbers” chart is not uniform.
The distribution of numbers in the “Random Numbers” table is uniform.
The distribution of numbers in the “Random Numbers” table is not uniform.
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a. (1 pt) Which hypothesis represents the claim? Circle one: Null Hypothesis (H0) or Alternative Hypothesis (Ha) |
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b. (2 pts) Verify that the conditions to use the Chi-Square Goodness-of-Fit test are met. |
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c. Test this hypothesis. (SHOW WORK TO EARN FULL CREDIT!) Fill in the table (2 pts). (ROUND TABLE VALUES TO TWO DECIMAL PLACES, AS NEEDED)
(2 pts) Clearly label a sketch with appropriate shading. Also, identify the Critical Value(s) and Test Statistic. (1 pt) Critical Value: _____________ (1 pt) Test Statistic: _____________ (2 pts) Would you reject or fail to reject the null hypothesis? Circle one: Reject H0 or Fail to Reject H0 Explain your choice: |
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d. (2 pts) Write a conclusion in the context of this problem. |