VOCAB
What is a single value estimate for a population parameter?
Point estimate
Which has a larger margin of error: a 99%, 95%, or 90% confidence interval based on the same raw data?
The 99% confidence interval would have the largest margin of error
what is the general equation you should ALWAYS write for the first step of the "do" step?
point estimate ± critical value (st error)
Do the STATE step only:
The recommended retail price of a brand of designer jeans is $150. The price of the jeans in a sample of 16 retailers is on average $141, with a sample standard deviation of $4. The prices can be assumed to be normally distributed. Construct a 95% confidence interval for the average sale price.
we will estimate μ=the true mean price of designer jeans at 95% confidence
Vegeta from Dragon Ball Z can't believe that the power level of Goku is "over" this value, in this famous early internet meme
What is 9000?
What is an interval or range of values used to estimate a population parameter?
Confidence Interval
These are the two ways we can shrink a margin of error
What is...
-Increase sample size and
-Decrease confidence level
A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours was recorded for each household in the sample for the first quarter of 2026. The average usage was found to be 375kWh with a standard deviation of 81kWh. Create a confidence interval for a 99% confidence level for the mean usage in the first quarter of 2026?
point estimate ± critical value (st error)
x-bar ± t* (sx/sqrt(n))
df=29
375 ± 2.756 (81/sqrt(30))
(334.24, 415.76)
Complete the STATE step only:
A Pew Research Center report on gamers and gaming estimated that 79% of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based on a random sample of 1400 U.S. adults. Construct a 95% confidence interval for the proportion of all U.S. adults who play video games.
Name the character in the image
Who is Salad Fingers?
C is the success rate (capture rate) of the method that produces the interval.
What is a confidence level
What is the z* for an 84% confidence interval for p
1.405
An industrial designer wants to determine the average amount of time it takes an adult to assemble an "easy to assemble" toy. A sample of 16 times yielded an average time of 19.92 minutes, with a sample standard deviation of 5.73 minutes. Provide a 95% confidence interval for the mean assembly time (assume all checks are passed).
point estimate ± critical value (st error)
x-bar ± t* (sx/sqrt(n))
df=15
19.92 ± 2.131 (5.73/sqrt(16))
(16.87, 22.97)
What are the three conditions we must check?
Random --> generalize to the population
Independent --> 10% condition
Normal --> Large Counts (10/10)/ CLT
In a viral World of Warcraft video, this player with what name charged into a high-level battle after being AFK during his raid groups complex planning session
Who is Leeroy Jenkins?
When asked to "construct and interpret" a confidence interval, what are the four steps you must follow? :
State, Plan, Do, Conclude (or choose, check, calculate, conclude)
What is the critical value for a 90% confidence interval for population mean with a sample size of 9?
t*=1.86
A Pew Research Center report on gamers and gaming estimated that 79% of U.S. adults play video games on a computer, TV, game console, or portable device such as a cell phone. This estimate was based on a random sample of 1400 U.S. adults. Construct a 95% confidence interval for the proportion of all U.S. adults who play video games.
point estimate ± critical value (st error)
p-hat ± z*sqrt((p-hat(1-p-hat)/n)
0.79 ± 1.96 sqrt(0.79*0.21/1400)
(0.77,0.81)
Complete the PLAN step only:
The recommended retail price of a brand of designer jeans is $150. The price of the jeans in a sample of 16 retailers is on average $141, with a sample standard deviation of $4. The prices can be assumed to be normally distributed. Construct a 95% confidence interval for the average sale price.
1-sample t-interval for μ
Random: SRS of 16 retailers
Normal: Population is approximately normally distributed, so ~Normal
Independent: 16 is less than 10% of designer jeans retailers
"New exciting flavors" of this item start out normal:
Rasberry. Cranberry. Apples. Cinnamon. Pecan.
Before becoming more absurdist, including:
Fish, Paperclip, Isreali-Palistinian conflict, Bits of glass, and FIRE!!
What are (Cunningham) Muffins?
What is the number of free choices left after a sample statistic is calculated? This is a value you only need for means-type problems
Degrees of freedom
We estimate with 95% confidence that between 81% and 87.4% of all adult residents of this city have cell phones.
What was the point estimate?
What was the margin of error?
point estimate=the average of 87.4 and 81:
(87.4+81)/2=84.2
Margin of error=87.4-84.2=3.2
A 2016 survey of 1480 randomly selected U.S. adults found that 55% of respondents agreed with the following statement: “Organic produce is better for health than conventionally grown produce."
Construct a 99% confidence interval for the proportion of all U.S. adults who think that organic produce is better for health than conventionally grown produce
point estimate ± critical value (st error)
p-hat ± z*sqrt((p-hat(1-p-hat)/n)
0.55 ± 1.645 sqrt(0.55*0.45/1480)
(0.53,0.57)
Complete the PLAN step only for this problem:
A 2016 survey of 1480 randomly selected U.S. adults found that 55% of respondents agreed with the following statement: “Organic produce is better for health than conventionally grown produce."
Construct a 99% confidence interval for the proportion of all U.S. adults who think that organic produce is better for health than conventionally grown produce
1-sample z-interval for p
random: SRS of 1480 US adults
Normal: .55*1480=814>10 and .45*1480=666>10 so ~Normal
Independent: 1480 is less than 10% of all US adults
This number, also noted by the singer of this song as his "girlfriend's age" and "my IQ" is how high the singer can count "alllll de way to"
Schfifty-five