Homework: z-Scores and Percentiles Assignment Instructions
Overview
This assignment allows you to demonstrate mastery of topics covered thus far. It specifically assesses ability to use SPSS, hand calculations, and tables to flexibly calculate and interpret scores in normalized units and percentiles.
Instructions
Download the Homework: z-Scores and Percentiles Assignment Template as a word document. Do not delete or modify the template, except to insert your answers where indicated. Use graduate-level writing skills and format using current APA conventions. Upload the completed file as a word document or PDF by its due date.
This assignment is worth a total of 50 points.
- Content: point values vary but are indicated in the template and total 40 points.
- Format: point values vary but are indicated in the template for 8 pts. The remaining 2 pts are for placing answers in the correctly designated spots within the template in a clear and easy to read format and uploading it in an approved format (word or PDF). Thus, the maximum is 10 points for format.
Note: Your assignment will be checked for originality via the Turnitin plagiarism tool.
z-Scores and Percentiles Template
This assignment is worth a total of 50 points.
- Content: point values vary but are indicated in the template and total 40 points.
- Format: point values vary but are indicated in the template for 8 pts. The remaining 2 pts are for placing answers in the correctly designated spots within the template in a clear and easy to read format and uploading it in an approved format (word or PDF). Thus, the maximum is 10 points for format.
Here is memory data from 30 students. Enter it into SPSS to complete the assignment.
| 8 | 6 | 7 | 5 | 5 | 2 |
| 5 | 6 | 8 | 5 | 3 | 9 |
| 6 | 9 | 5 | 9 | 7 | 3 |
| 6 | 5 | 6 | 4 | 8 | 6 |
| 8 | 7 | 10 | 6 | 6 | 6 |
| Question #1
Run descriptive statistics to obtain the needed mean and standard deviation and other information to determine whether the data is normally distributed. Make sure to “save standardized values” when doing so. Copy / Paste the output here, formatting using professional conventions, numbering it as Table 1 and giving it an appropriate title (no Note needed). (4 pts content / 2 pts format) z-Scores and Percentiles Assignment |
<answer here>
| Question #2 Write a brief description of the memory scores obtained from this sample as you would in a Method section of a research report. Make sure to include the mean, standard deviation, and whether the data appears normally distributed (use skew and kurtosis values to determine this). Use proper APA format as shown in previous weeks. (4 pts content / 2 pts format) z-Scores and Percentiles Assignment |
<answer here>
| Question #3
Create an appropriate figure to examine the distribution of memory scores in the sample (make sure both axes titles are in Title Case!). Number it Figure 1 and create an appropriate title. In the Note section, using both a visual inspection of the data and a skewness statistic to discuss whether the distribution is normal. Make sure all components are formatted using APA conventions. (4 pts content / 2 pts format) z-Scores and Percentiles Assignment |
<answer here>
| Question #4
Continuing to use this dataset, go to Variable View, create a third variable and name it “percRank”. Make sure it is numeric with measure set to “Scale”. Have SPSS compute the percentile ranks based on the normal distribution, using the Mean and Standard Deviation shown in your output from Question #1. Take a snapshot of your data view and place it below so that all three columns can be seen in their entirety. (It does not need to be in APA format). (2 pts content / 2 pts format) |
<answer here>
| Question #5 Assuming a normal distribution, use the data from your answer above to answer the following questions: (3 pts each = 12 pts Content)
z-Scores and Percentiles Assignment |
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| Identify all memory scores in the data set that are above the 80th percentile. | <answer here> |
| Are the corresponding z scores below zero, near zero, or above zero? Why (discuss in relation to the mean)? | <answer here> |
| Identify all scores that are in the bottom 10th percentile. | <answer here> |
| Are the corresponding z scores below zero, near zero, or above zero? Why (discuss in relation to mean)? | <answer here>
z-Scores and Percentiles Assignment |
| Question #6 Assuming a normal distribution, use the mean and standard deviation you obtained from the SPSS output in previous sections to answer the following questions:
Note: you MUST show all work to be eligible for credit. Round to 2 decimals for z score; do NOT round for proportion – use all 4 decimals as shown in Appendix C.3. (3 pts each = 6 pts Content)
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| For a memory score of 7, calculate the z-score, and find the proportion of the distribution located up to this point |
| Calculate and show all work: z-Scores and Percentiles Assignment
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| Given the z score you calculated for a memory score of 7, find the proportion of the distribution located up to this point. (Hint: remember if the z score is above the mean, you’ll need to add 0.50!) |
| Calculate and show all work: z-Scores and Percentiles Assignment
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| Question #7 Assuming a normal distribution, use the mean and standard deviation you obtained from the SPSS output in previous sections to answer the following questions:
Note: you MUST show all work to be eligible for credit. Round to 2 decimals for z score; do NOT round for proportion – use all 4 decimals as shown in Appendix C.3. (4 pts each = 8 pts Content)
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| For a memory score of 5, calculate the z-score. |
| Calculate and show all work: z-Scores and Percentiles Assignment
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| Given the z score you calculated for a memory score of 5, find the proportion of the distribution located up to this point. **Think about what C.3 provides (area between the mean and z) and where your point would fall on the normal distribution. You will need to subtract the number you find in the table from 0.5 to answer this question. Do NOT round – show all work – final answer should have 4 decimal places. |
| Calculate and show all work: z-Scores and Percentiles Assignment
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