p-hats, pie charts, sample size and statistics

J. Hathaway

Lesson Outcomes

  1. Calculate and interpret a sample proportion
  2. Summarize categorical data with a bar or pie chart
  3. Determine the mean, standard deviation, and shape of a distribution
  4. Calculate probabilities using a distribution of sample proportions

Why do people make charts of data?

Socrative Quiz (BYUICLASS): L16 Data Viz questions

Pie Charts (BYUICLASS)

Bar Charts (BYUICLASS)

The only thing worse than a pie chart is several of them. (Edward Tufte)

Who is Edward Tufte?

Visualizing data example

Understanding One Sample Proportion Tests

What are the differences from what we’ve previously learned? (Q8-Q11)

\(z = \frac{\hat{p} - p }{\sqrt{\frac{p(1-p)}{n}}} = \frac{0.5 - 0.48}{\sqrt{\frac{0.48(1-0.48)}{1041}}} = 1.292\)

If we are estimating the proportion with data, why are we using the z-distribution?

\(z = \frac{\hat{p} - p }{\sqrt{\frac{p(1-p)}{n}}}\)

  • Do we have to estimate our standard deviation under the null hypothesis?

What happens to our proportion standard deviation for different assumed means?

  • First, What is the proportion standard deviation?

\(\hat{p} = \sqrt{\frac{p(1-p)}{n}}\)

Understanding np and N(1-p) rule as a check for normality (Q12-13)

For each case below

  1. use a number line from 0 to 1.
  2. Calculate your standard devation of p.
  3. Use the p and standard deviation of p to draw the normal curve on your number line.
  • Case 1: n = 25 and p = 0.975
  • Case 2: n = 400 and p = 0.975