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Module 5/6; Creating inferential Statistics report

I. Introduction

a. The purpose of the survey conducted by group one was to obtain and evaluate how much sleep that night          shift workers slept prior to working the night shift, and how many hours were slept when not working the          night shift. People surveyed were friends, colleagues, acquaintances, and even a few strangers. The                  population that were interviewed were night shift working adults, both male and female. The survey was          voluntary and questions were asked through social media, face to face, email...

b. The four survey questions used are stated below:

1. Do you prefer to work the night shift?  Y/N

2. How many hours so you sleep prior to your shift?  _____hours.

3. How many hours do you sleep when you are not working?  _____hours.

4. Describe how you feel while you are at work (Select One): Extremely tired, Moderately tired, Somewhat            tired, Full of energy.

II. Looking at a Categorical Variable

a. I have chosen the yes/no question, as I believe this may influence the amount of sleep and individual               may or may not get if the night shift is or is not a preferred shift. The question is as follows: "Do you                 prefer to work the night shift?" The response can be seen in the pie chart below.

Result 1: Pie Chart With Data (module 5/6)   [Info]

From the pie chart we can see that 12 individuals, or 60% of individuals out of 20, do not prefer to work the night shift. While only 8 out of 20 individuals, or 40% did prefer to work the night shift.

b. The next two results shown are a 95% confidence interval for the proportion of the population that answered "yes and no"  to the question, "Is this your preferred shift?" I am showing both results, as I found it interesting that the margin of error E computed the same number for both the yes and no answer. I will however interpret for the "yes" answer only.

Result 2: One sample proportion confidence interval 95% (module 5/6)   [Info]

### One sample proportion confidence interval:

Outcomes in : Do you prefer to work the night shift?
Success : Yes
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:
VariableCountTotalSample Prop.Std. Err.L. LimitU. Limit
Do you prefer to work the night shift?8200.40.109544510.18529670.6147033

Result 3: One sample proportion confidence interval, 95% (module 5/6)   [Info]

### One sample proportion confidence interval:

Outcomes in : Do you prefer to work the night shift?
Success : No
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:
VariableCountTotalSample Prop.Std. Err.L. LimitU. Limit
Do you prefer to work the night shift?12200.60.109544510.38529670.8147033

Interpretation of the confidence interval: The confidence interval was based on 20 samples, n=20, using the yes/no question. A 95%confidence interval was used in obtaing the results, with p being the population proportion of night shift workers who prefer to work the night shift. A 95% confidence interval is an estimated range that states you can be 95% certain that it contains the  population mean. Larger samples are more accurate than smaller samples and a 95% confidence interval should not be mistaken for 95% probability. The confidence interval can be seen in the data as the Lower Limit (.1852967) and the Upper Limit (.6147033). The data results state that we are 95% confident that our proportion of the population that answered "yes" to our question is between 0.1852967 and 0.6147033. To find the margin of error E= 0.1852967-0.6147033/2=-0.2147033.

III. Looking at a Numerical Variable

a. The question used for the next section is: "How many hours do you sleep prior to your shift?" These are the results for the 86 individuals interviewed, and can be seen below in the histogram and the summary statistics (please only refer to the top line of the summary statistics; "How many hours do you sleep prior to your shift?").

Result 4: Histogram of hours slept prior to working   [Info]

Result 5: Summary Stats of hours slept prior to working vs hours slept when not working   [Info]

### Summary statistics:

Hrs slept prior to working865.44186054.01422712.00355360.2160487469094.574682.53.967551.99187136.817438-1.0235681.21232556
Hrs slept when not working867.91860471.78741451.33694220.144166198841278.56811.51.76663061.329146616.8835580.49973051.52897118

b. A 95% confidence interval for the population is shown below.

Result 6: One sample T confidence interval (module 5/6)   [Info]

### One sample T confidence interval:

μ : Mean of variable

95% confidence interval results:
VariableSample MeanStd. Err.DFL. LimitU. Limit
How many hours do you sleep prior to working your shift?5.2250.20350546194.79905825.6509418

Interpretation of the Confidence Interval: A 95% confidence interval was used for the population mean. The sample size, n=20 and the degrees of freedom, n-1 = 20-1=19. I chose to use a t-interval instead of a z- interval because the standard deviation is not known and we see/use the standard of error instead. Also, a z-interval is used when there is a large sample size and the t-interval is used when degrees of freedom n is small, such as n