Understanding of the Logic of the Normal Curve and Areas Under Segments of That Curve - Science and Maths Assignment Help

Assignment Task:

Task:

PART I: 
Task 1:  Individual normal distribution scores.
You will need the “Normal Distribution Table” for this (text, p. 111).
 

Objectives:

•  Ascertain your understanding of the logic of the normal curve and areas under segments of that curve
•  Test your ability to calculate relevant Z-Scores
•  Test your ability to translate Z-Scores into percentiles

I recommend that you use some variation of the attached charts to mark the placement of the Z-scores that you derived from the ratings.  These
should help you to see if the percentages should be higher or lower than 50%.  They are formatted in MS WORD so that you can easily adjust cutoff
lines and arrows.

After the presidential vote was over, a group of voters was asked to judge the character of the campaign.  A 0% indicates deep dissatisfaction, 50%
neutral, and 100% utter and blissful satisfaction (we can assume drugs are involved here).  The mean for this group is 43% with a standard deviation of 14.6%. 

Assume that satisfaction ratings for this group are normally distributed. Task 1 answers should only relate to describing the cutoffs within this group,
not a projection to a broader population.

1. What percentage rated the campaigns above a low ‘C’ or 70%?
2. What percentage were so disgusted that they rated the campaigns no better than 30%? (10)

Make sure that you pay attention to what each of the above is asking (‘no better’, ‘above’, etc.). Also, don’t just give us the percent, demonstrate that
you know how to derive those percentages.

You may use this graph to mark off your cutoffs and demonstrate what is above or below that value.

Task 2:  Distribution of sample means
Objectives:

•  Judge your understanding of the concept of mean inference and how it applies to inferring a range of population parameters from a sample
•  Test your ability to calculate margins of error and mean parameters
•  Judge whether you understand what can and cannot be confidently rejected (Ho)
•  Make sure you understand the importance of sample size

Same scenario, but this time that group is a random sample drawn from the entire voting population.  The size of the sample is 750 (N).  Using our two curve (Chapter 6) 95% confidence limit test:

1. What would we estimate the true mean rating to be from the population from which this sample was randomly drawn?    
2. What population mean values can we confidentially (95%) reject as possibilities?  Use a phrase such as “any value above… or….”. 
3. Might the sample have been randomly drawn from a population outside of that estimated range?  Why or why not? 

For the two?curve items, just type in your values under the vertical lines as in the text. Make sure to show your calculations first:

Task 1:
Before testing your hypotheses (from Assignment 1) inferentially, let’s all first run a simple analysis to determine whether or not your feeling thermometer means (both IV groups combined) are significantly different from neutral (50°). The mean for all respondents (including all
generations, not just the two I selected) for my example DV, Obama (V15) is slightly on the warm side (53.52°). You will do this for both V16 and
V17.

Task 2:
Here you will be testing whether or not the differences that you calculated in Assignment 1 could be attributed to the random luck of the draw. That is could your two groups have had equal mean ratings on each variable in the population from which this sample was drawn? The null hypothesis now is: for, separately, V16 and V17.

ANALYSIS:

•  Using the ‘Independent Samples T-Test’ procedure (T-TEST GROUPS, Form 3), determine whether or not you can reject the aforementioned null hypothesis.
• Answer all the following. All your answers should lead to the same conclusion for each DV—you can either confidently reject or not confidently reject the null hypothesis that the true population mean difference between your two IV groups is 0°.
•  A-C. What is the mean difference between your two IV groups in their assessment of Clinton (V16)? This should match what you found in Assignment 1.
•  A-T. What is the mean difference between your two IV groups in their assessment of Trump (V17)? This should match what you found in Assignment 1.
•  B-C. Can you confidently reject the possibility (null hypothesis) that the difference between the means of your two IV categories on V16 is 0 degrees in the population from which this sample was drawn? Why or why not?
•  B-T. Can you confidently reject the possibility (null hypothesis) that the difference between the means of your two IV categories on V17 is 0 degrees in the population from which this sample was drawn? Why or why not?
•  C-C. What is your estimated range of the actual population difference between your two IV groups for V16? You should have both a low and high figure estimate.
•  C-T. What is your estimated range of the actual population difference between your two IV groups for V17? You should have both a low and high figure estimate.

Task 3:
Copy all the relevant tables to a WORD or WORD-translatable file, along with your discussion and answers to all of the questions above. Sum up with a final analysis of the specified hypothesized relationships. Submit through the Assignment drop box set up on CANVAS. Be as detailed as possible.

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