Dataset: 13, 7, 6, 12, 0, 4

Provide the following: *ΣX*, *M*, *s*2, *s, sM, t*

By hand: show your work and upload a picture (non-Mac files, please)

In SPSS: conduct a one-sample *t*-test -- no need to use hypothesis testing steps for this activity

Lastly: upload screenshots of your work by hand, your data view, and output files -- no annotation needed

To solve this problem, we need to find the following values for the given dataset: 13, 7, 6, 12, 0, 4.

### By hand calculations:

1. **ΣX (Sum of all values)**  
   The sum of all values in the dataset:
   \[
   ΣX = 13 + 7 + 6 + 12 + 0 + 4 = 42
   \]

2. **M (Mean or average)**  
   The mean (M) is the sum of all values divided by the number of values:
   \[
   M = \frac{ΣX}{N} = \frac{42}{6} = 7
   \]

3. **s² (Sample variance)**  
   The sample variance is the average of the squared differences from the mean. First, calculate the squared differences for each data point from the mean \( M \):

   \[
   \text{Squared differences: } (13 - 7)^2, (7 - 7)^2, (6 - 7)^2, (12 - 7)^2, (0 - 7)^2, (4 - 7)^2
   \]
   \[
   = 36, 0, 1, 25, 49, 9
   \]

   Now, the sample variance \( s^2 \) is calculated by summing these squared differences and dividing by \( N - 1 \) (degrees of freedom):
   \[
   s^2 = \frac{36 + 0 + 1 + 25 + 49 + 9}{5} = \frac{120}{5} = 24
   \]

4. **s (Standard deviation)**  
   The standard deviation is the square root of the sample variance:
   \[
   s = \sqrt{24} \approx 4.899
   \]

5. **sM (Standard error of the mean)**  
   The standard error of the mean is the sample standard deviation divided by the square root of the sample size:
   \[
   sM = \frac{s}{\sqrt{N}} = \frac{4.899}{\sqrt{6}} \approx \frac{4.899}{2.449} = 2.0
   \]

6. **t (t-value for a one-sample t-test)**  
   The formula for the t-value is:
   \[
   t = \frac{M - \mu}{sM}
   \]
   Here, \( \mu \) is the population mean, which is typically provided for a one-sample t-test. If it is not specified, you can choose a reasonable comparison value. For now, let’s assume \( \mu = 0 \) for demonstration:
   \[
   t = \frac{7 - 0}{2.0} = 3.5
   \]

### SPSS One-Sample t-Test:
You can conduct a one-sample t-test in SPSS as follows:
1. Enter the dataset into SPSS (values: 13, 7, 6, 12, 0, 4).
2. Go to **Analyze > Compare Means > One-Sample T-Test**.
3. In the dialog box, select the variable and enter the test value (let's assume the test value is \( \mu = 0 \)).
4. Run the analysis.

This will generate output including the t-value, degrees of freedom, and p-value.

### Screenshots and Upload:
Since you want me to show hand-written work and screenshots from SPSS, I can't do this within my environment. However, you can replicate these steps and upload images of your work using any non-Mac image format (such as PNG or JPEG).

Feel free to upload your photos and screenshots if you'd like me to review them.

---

Let me know if you'd like more details on any step! Here are 5 related questions:

1. How does changing the population mean (\( \mu \)) in a t-test affect the t-value?
2. What is the significance of degrees of freedom in calculating sample variance?
3. How would you interpret the results from an SPSS one-sample t-test?
4. What is the relationship between sample size and standard error?
5. How do you interpret a t-test when the p-value is less than 0.05?

**Tip:** SPSS allows for easy visualization of data distributions. Always explore descriptive statistics before running tests.

User Problem-The query submitted by the user:Dataset: 13, 7, 6, 12, 0, 4. Provide the following: ΣX, M, s², s, sM, t. By hand: show your work and upload a picture (non-Mac files, please). In SPSS: conduct a one-sample t-test -- no need to use hypothesis testing steps for this activity. Lastly: upload screenshots of your work by hand, your data view, and output files -- no annotation needed.

Calculate ΣX, M, s², s, sM, and t for the dataset 13, 7, 6, 12, 0, 4. This guide includes detailed hand calculations and instructions for performing a one-sample t-test in SPSS. Ideal for students learning statistical methods, including mean, variance, standard deviation, and t-tests.

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