SWBAT: Construct and interpret a confidence interval for a population proportion.
Do Now:
A biologist has taken a random sample of a specific type of fish from a large lake. A 95
percent confidence interval was calculated to be 6.8 ± 1.2 pounds. Which of the
following is true?
(A) 95 percent of all the fish in the lake weigh between 5.6 and 8 pounds.
(B) In repeated sampling, 95 percent of the sample proportions will fall within 5.6 and 8 pounds.
(C) In repeated sampling, 95% of the time the true population mean of fish weights will be equal
to 6.8 pounds.
(D) In repeated sampling, 95% of the time the true population mean of fish weight will be
captured in the constructed interval.
(E) We are 95 percent confident that all the fish weigh less than 8 pounds in this lake.
Confidence Intervals: Population Proportion
Formula:
Steps:
1. Check conditions (random, normal, independent)
2. Find p-hat
3. Find SD of p-hat
4. Determine the critical value from the t-table (z*)
5. Use formula to find lower and upper bound of interval
6. INTERPRET!!
SWBAT: Construct and interpret a confidence interval for a population proportion.
1) If we randomly select the 2009 regular season, it shows that catcher Joe Mauer of the
Minnesota Twins had 191 hits in 523 at-bats.
(a) What was Maurer’s proportion of hits in the 2009 regular season?
(b) Calculate a 95% confidence interval for Mauer’s ability to get a hit in his career so far and
interpret the interval in the context of the problem.
(c) Does the interval give convincing evidence that Mauer’s ability to get a hit is greater than
0.300? Explain.
SWBAT: Construct and interpret a confidence interval for a population proportion.
2) If we randomly select the 2009 regular season, it shows that then quarterback Peyton
Manning of the Indianapolis Colts attempted 571 passes and completed 393 of them.
(a) What was Manning’s completion rate in the 2009 regular season?
(b) Calculate a 95% confidence interval for Manning’s ability to complete a pass in in his career
so far and interpret the interval in the context of the problem.
(c) Does the interval give convincing evidence that Manning’s ability to complete more than
two-thirds of his passes? Explain.
SWBAT: Construct and interpret a confidence interval for a population proportion.
3) If we randomly select the 2009 regular season, it shows that Arizona Diamondbacks
outfielder Justin Upton had 158 hits in 526 at-bats.
(a) Calculate and interpret a 90% confidence interval for Upton’s ability to get a hit.
(b) What does it mean to be 90% confident?
(c) How could you make the margin of error smaller? Are there any drawbacks to this?
SWBAT: Construct and interpret a confidence interval for a population proportion.
4) If we randomly select the 2009 regular season, it shows that Alex Ovechkin of the
Washington Capitals had 50 goals in 368 attempts.
(a) Calculate and interpret a 96% confidence interval for Ovechkin’s ability to make a goal.
(b) What does it mean to be 96% confident?
(c) If you wanted to be more than 96% confident, how would you change the interval you
calculated in part (a)? Are there any drawbacks to this? Can you be 100% confident?