6.1 - Review
     » Descriptive Statistics – a summary or 
      description of data (usually the calculation)
       ˃ Ex) The mean grade for Ms. Halliday’s CHS Statistics students 
        on the 5.1 – 5.4 Quiz was 89.1.  (89.1 is the descriptive statistic)
     » Inferential Statistics – when we use sample data 
      to make generalizations (inferences) about a 
      population
       ˃ We use sample data to:
         + Estimate the value of a population parameter
         + Test the claim (or hypothesis) about a population
       ˃ Chapter 6 is dedicated to presenting the methods for 
        determining inferential statistics. 
     Warm-Up
      » Here is a list of 99 body temperatures obtained by the University of 
         Maryland.  Calculate the descriptive statistics for these data (mean, 
         standard deviation, sample size). Discuss the shape, center, and spread, 
         as well as any outliers.  
          98.698.698.098.099.098.498.498.498.498.698.698.898.6     97.097.0
      98.897.697.798.897.697.798.898.098.098.398.5     97.398.797.498.998.6
      99.597.597.397.698.299.698.796.4     98.598.098.698.697.298.498.698.2
      98.097.898.098.498.6     98.697.899.096.597.698.096.997.697.197.998.4
      97.398.0    97.597.698.298.598.898.797.898.097.197.499.498.498.6 
      98.498.598.698.398.798.697.197.998.898.797.698.299.2     97.898.098.4
      97.898.497.498.097.0
   Estimating Population Mean
   The Central Limit Theorem told us that the sampling distribution 
   »  
   model for means is Normal with mean μ and standard deviation 
   » All we need is a random sample of quantitative data.
   » And the true population standard deviation, σ.
     ˃ Well, that’s a problem…
   » We’ll do the best we can: estimate the population parameter σ 
     with the sample statistic s.
   » Whenever we estimate the standard deviation of a 
     sampling distribution, we call it a standard error.
   » Our resulting standard error is SE(
   Confidence Intervals
   » A confidence interval uses a sample statistic to 
     estimate a population parameter.
      ˃ In other words, a confidence interval uses a sample mean and standard 
       deviation to estimate the population mean for that particular populations 
       of interest.
   » But, since samples vary, the statistics we use, and 
     thus the confidence intervals we construct, vary as 
     well.
   Confidence Intervals
   »» B  y the 68-95-99.7% Rule, we know
      ˃ about 68% of all samples will have  ’s within 1 SE of 
      ˃ about 95% of all samples will have ’s within 2 SEs of 
      ˃ about 99.7% of all samples will have ’s within 3 SEs of 
   » Consider the 95% level: 
      ˃ There’s a 95% chance that is no more than 2 SEs away from . 
      ˃ So, if we reach out 2 SEs, we are 95% sure that  will be in that interval. In 
       other words, if we reach out 2 SEs in either direction of , we can be 95% 
       confident that this interval contains the true parameter mean.
   » This is called a 95% confidence interval.