In this unit we have worked with scores and their locations within a distribution. This discussion is designed to get you to think a little more about distributions of scores. Shown below are two samples of scores. Input these scores into SPSS and use plots and data descriptions to see if you can guess which sample of scores is a random sample of scores from a population that has a normal distribution with a mean of 80 and a standard deviation of 20. Leave a discussion message that describes your methods and whether you think sample A or sample B is most likely to have come from the population I just described. Explain your reasons. Check back to see if your classmates arrived at the same conclusion. After reading several other posts describe why you would stick with your original answer or change it now that you’ve read answers from other people.
Sample A
94
97
79
81
73
109
73
90
70
74
Sample B
65
95
63
87
79
85
68
103
96
67
87
87
69
80
112
98
73
87
84
117
To determine which sample of scores is most likely to have come from a population with a normal distribution, mean of 80, and standard deviation of 20, we can use SPSS to create plots and compute relevant statistics.
Here's how you can proceed:
1. Open SPSS and enter the scores for Sample A and Sample B into two separate columns in the Data View.
2. Go to the Graphs menu and choose Legacy Dialogs > Histogram.
3. Select the variables containing the scores for Sample A and Sample B, and click OK. This will create histograms for each sample, allowing us to visually examine their distributions.
4. Take note of the shape of the histograms. If the distribution of scores in a sample closely resembles a bell-shaped curve, it suggests a normal distribution.
5. Next, calculate the descriptive statistics for each sample. Go to the Analyze menu and choose Descriptive Statistics > Descriptives.
6. Select the variables representing Sample A and Sample B, and click OK. This will provide us with the mean and standard deviation for each sample.
7. Compare the descriptive statistics of each sample to the population characteristics (mean = 80, standard deviation = 20). Look for close matches or similarities.
Based on the provided instructions, analyze the histograms and the descriptive statistics to draw your conclusion about which sample is most likely to have come from a normally distributed population.
Once you have reached your conclusion, leave a discussion message stating your methods and your choice (Sample A or Sample B) along with your reasons for making that choice.
After reading other classmates' posts, consider their arguments and evidence. Decide whether you want to stick with your original answer or change it based on their perspectives. Take into account any strong arguments or convincing evidence presented by your classmates.
Remember, the goal is to weigh the visual representation of the distributions (histograms) and the descriptive statistics against the known characteristics of the population distribution.
To determine which sample is more likely to have come from a population with a normal distribution, we can analyze the data using SPSS and examine plots and data descriptions. Here's a step-by-step guide on how to do this:
Step 1: Input the scores for Sample A and Sample B into SPSS. Create two separate variables for each sample.
Step 2: Once the data is entered, we can generate descriptive statistics for each sample. This will provide us with measures such as mean, standard deviation, and other key statistics. Follow these steps to compute descriptive statistics:
- Go to the "Analyse" menu.
- Select "Descriptive Statistics" and then choose "Frequencies".
- Move the variables of each sample into the "Variable(s)" box.
- Click "OK" to generate the statistics.
Step 3: After obtaining descriptive statistics, we can examine the measures of central tendency and variability. Pay attention to the mean and standard deviation values for each sample.
Step 4: Next, let's create a histogram for each sample to visualize the distributions. We can follow these steps:
- Go to the "Graphs" menu.
- Select "Legacy Dialogs" and then choose "Histogram".
- Move the variables of each sample into the "Variable(s)" box.
- Click "Ok" to generate the histograms.
Step 5: Analyze the histograms for any indications of normal distribution. Look for symmetrical shapes, bell curves, and the absence of significant outliers.
Step 6: Finally, compare the statistics and histograms for Sample A and Sample B to determine which one is more likely to have come from a population with a normal distribution.
After analyzing the data, I would not be able to determine which sample is more likely without actually performing the above steps in SPSS. However, based on intuition, I would expect Sample B to be more likely to have come from a population with a normal distribution. This is because Sample B has a wider range of scores distributed across a wider range of values, while Sample A seems to have more scores clustered around the mean.
Please note that this is just speculation and the actual analysis in SPSS would provide more accurate information.