Unit 3 REVIEW

•  Writing Conclusions: DO NOT choose statements about individuals or other sample means
• "...the true percentage" = one proportion test
• correct or incorrect, yes or no response, etc. means it is categorical.
• Which will NOT reduce the size of the margin of error?
• Increase sample size
• Increase confidence level
• Decrease st. dev.
• Decrease confidence level

Lesson 16 Recap

• Pie charts are used when you want to represent the observations as part of a whole, where each slice (sector) of the pie chart represents a proportion or percentage of the whole.

• Bar charts present the same information as pie charts and are used when our data represent counts. A Pareto chart is a bar chart where the height of the bars is presented in descending order.

• p^$\stackrel{<br>}{\mathrm{<br>}}$ is a point estimator for true proportion. p^=xn${\displaystyle \stackrel{<br>}{\mathrm{<br>}}}$

• The sampling distribution of p^$\stackrel{<br>}{\mathrm{<br>}}$ has a mean of p$\mathrm{<br>}$ and a standard deviation of p⋅(1−p)n−−−−−−−−−√
  
  
  
  
   

• If np≥10$<br>$ and n(1−p)≥10, you can conduct probability calculations using the Normal Probability Applet.

  z=value−meanstandard deviation=p^−pp⋅(1−p)n−−−−−√
  
  

Lesson 17 Recap

• The estimator of p$\mathrm{<br>}$ is p^$\stackrel{<br>}{\mathrm{<br>}}$. p^=xn${\displaystyle \stackrel{}{<br>}}$ and is used for both confidence intervals and hypothesis testing.

• You will use the Excel spreadsheet Math 221 Statistics Toolbox, to perform hypothesis testing and calculate confidence intervals for problems involving one proportion.

• The requirements for a confidence interval are np^≥10 and n(1−p^)≥10
  . The requirements for hypothesis tests involving one proportion are np≥10
   and n(1−p)≥10
  .

• We can determine the sample size we need to obtain a desired margin of error using the formula n=(z∗m)2p∗(1−p∗)${\displaystyle {\mathrm{<br>}}^{}{\mathrm{<br>}}^{<br>}}$ where p∗
   is a prior estimate of p$\mathrm{<br>}$. If no prior estimate is available, the formula (z∗2m)2${\displaystyle {\mathrm{<br>}}^{}}$ is used.
  

Lesson 18 Recap

• When conducting hypothesis tests using two proportions, the null hypothesis is always p1=p2
  , indicating that there is no difference between the two proportions. The alternative hypothesis can be left-tailed (<$<$), right-tailed(>$>$), or two-tailed(≠$\ne$).

• For a hypothesis test and confidence interval of two proportions, we use the following symbols:

  Sample proportion for group 1:Sample proportion for group 2:p^1=x1n1p^2=x2n2$$\begin{array}{lc}\text{<br>}& \end{array}$$
  
  

• For a hypothesis test only, we use the following symbols:

Overall sample proportion:p^=x1+x2n1+n2$$\begin{array}{lc}\text{<br>}& \end{array}$$

• Whenever zero is contained in the confidence interval of the difference of the true proportions we conclude that there is no significant difference between the two proportions.

• You will use the Excel spreadsheet Math 221 Statistics Toolbox to perform hypothesis testing and calculate confidence intervals for problems involving two proportions.
  

Lesson 19 Recap

• The χ2${\mathrm{<br>}}^{\mathrm{<br>}}$ hypothesis test is a test of independence between two variables. These variables are either associated or they are not. Therefore, the null and alternative hypotheses are the same for every test:

  H0:Ha:The (first variable) and the (second variable) are independent.The (first variable) and the (second variable) are not independent.$$\begin{array}{cl}{\mathrm{<br>}}_{}& \end{array}$$
  
  

• The degrees of freedom (df$\mathrm{<br>}$) for a χ2${\mathrm{<br>}}^{\mathrm{<br>}}$ test of independence are calculated using the formula df=(number of rows−1)(number of columns−1)
  

• In our hypothesis testing for χ2${\mathrm{<br>}}^{\mathrm{<br>}}$ we never conclude that two variables are dependent. Instead, we say that two variables are not independent.