Exam 2 Modules 11 to 19

  • Due Jul 15, 2024 at 8pm
  • Points 18
  • Questions 36
  • Available Jul 15, 2024 at 6:15pm - Jul 15, 2024 at 8pm 1 hour and 45 minutes
  • Time Limit 100 Minutes

Instructions

Copy the following formulas for use during the exam.  Make sure to scroll down to see all formulas provided.

Formula for Expected Value is  The mean equals the sum of the values of x times their probabilities.

 

For a normal curve, the Empirical Rule tells us that there is a 68% chance that observations fall within 1 standard deviation of the mean, 95% within 2 standard deviations of the mean, and 99.7% within 3 standard deviations of the mean.

To summarize using probability notation:

  1. LaTeX: P\left(\mu_x-\sigma<X<\mu_x+\sigma\right)=0.68
  2. LaTeX: P\left(\mu_x-2\sigma<X<\mu_x+2\sigma\right)=0.95
  3. LaTeX: P\left(\mu_x-3\sigma<X<\mu_x+3\sigma\right)=0.997

These three facts together are called the empirical rule for normal curves.

For quantitative data:

Z equals open parenthesis x minus mu close parenthesis divided by sigma

 

For categorical data:

LaTeX: standard\:error\:=\:\sqrt{\frac{p\left(1-p\right)}{n}}

LaTeX: Z\:=\:\frac{statistic\:-\:parameter}{standard\:error}=\frac{\hat{p}-p}{standard\:error};     

 LaTeX: Z=\frac{\hat{p}-p}{\sqrt{\frac{p\left(1-p\right)}{n}}}

the formula for a confidence interval: Point Estimate+/- Margin of Error ========> p ̂±Zc √((p ̂(1-p ̂))/n)

For our most common confidence levels, the values of Zc are:

  • 90% confidence interval: Zc≈ 1.645
  • 95% confidence interval: Zc≈ 1.960 (2 is a rough approximation; 1.960 is more accurate)
  • 99% confidence interval: Zc≈ 2.576

 For the test statistic which is the z-score for the sample proportion. The formula is:

LaTeX: Z=\frac{\hat{p}-p}{\sqrt{\frac{p\left(1-p\right)}{n}}}                    

 

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