Vocab & Notation
On your whiteboard, draw the symbol for sample proportion.
\hat{p}
An EV manufacturing plant tests a sample of 36 batteries from a batch to measure their single-charge driving range. The sample yields a mean range of 310 miles with a standard deviation of 12 miles.
What is the point estimate?
\bar{x}=310
An EV manufacturing plant tests a sample of 36 batteries from a batch. They find that 18 of the batteries exceed the baseline energy-density standard.
What is the point estimate?
\hat{p}=0.50
On your white board, draw a normal curve!
Up to teacher.
Define confidence interval
A confidence interval is a range of values, calculated from sample data, that is likely to contain the true value of an unknown population parameter
An EV manufacturing plant tests a sample of 36 batteries from a batch to measure their single-charge driving range. The sample yields a mean range of 310 miles with a standard deviation of 12 miles.
Construct a 95% confidence interval for the true population mean driving range. No sentence necessary.
310 \pm 3.92 = (306.08, 313.92)
An EV manufacturing plant tests a sample of 36 batteries from a batch. They find that 18 of the batteries exceed the baseline energy-density standard. Construct a 95% confidence interval for the true population proportion, no sentence necessary. Round to 4 decimal places.
0.50 \pm 0.1633 = (0.3367, 0.6633)
On your white board, draw a skewed to the left distribution and a skewed to the right distribution. Label which is which!
Up to teacher.
Define point estimate
a single numerical value calculated from sample data to serve as your "best guess" for an unknown population parameter.
A tech company tests a sample of 25 smartphones to measure battery life under heavy use. The sample yields a mean battery life of 50 hours with a standard deviation of 15 hours.
Construct a 90% confidence interval for the true population mean battery life. No sentence necessary.
50 \pm 4.95 = (45.05, 54.95)
A tech company tests 25 smartphones under heavy use. They find that 10 of the phones retained over 80% battery life after 24 hours.
Construct a 95% confidence interval for the true population proportion, no sentence necessary. Round to 4 decimal places.
0.40 \pm 0.1921 = (0.2079, 0.5921)
Define sample and population, provide an example.
Population: The entire group of individuals, items, or measurements that you want to draw conclusions about.
Sample: A smaller, representative subgroup selected from the population to collect data from.
On your whiteboard, write the symbols for sample mean & population mean. Label which is which.
Population mean:
\mu
Sample mean:
\bar{x}
A shipping warehouse tests a sample of 64 delivery trucks to measure the time required to complete a daily route. The sample yields a mean delivery time of 120 minutes with a standard deviation of 24 minutes.
Construct a 99% confidence interval for the true population mean delivery time. Give your final answer in the form of a sentence!
We are 99% confident that the true average delivery time is between 112.26 and 127.74 minutes.
A shipping warehouse inspects a sample of 64 delivery trucks. They find that 16 of the trucks completed their route ahead of schedule.
Construct a 99% confidence interval, write your final answer in the form of a sentence! Round to 4 decimal places.
We are 99% confident that the true proportion of trucks finishing early is between 11.04% and 38.96%.
At a video game arcades competition, player scores are normally distributed with a mean score of 800 points and a standard deviation of 50 points.
Leo scored 900 points on his game! What is the z-score for Leo's game score?
z = 2
Define margin of error and describe how it is used to construct a confidence interval.
The margin of error is a statistic that quantifies the maximum expected difference between a sample result and the true population value due to random sampling variations.
It is used to construct a confidence interval by acting as the plus-or-minus range centered around a sample statistic (like a mean or proportion).
A sports analytics team tests the sprint speed of a sample of 30 professional soccer players. The sample yields a mean top speed of 21.47 mph with a standard deviation of 2.83 mph.
Construct a 90% confidence interval for the true population mean top speed. Give your final answer in the form of a sentence!
We are 90% confident that the true average top speed for players in this league is between 20.62 and 22.32 mph.
A civil engineering firm tests a sample of 42 test pillars on a bridge project. They find that 18 pillars show minor surface weathering.
Construct a 95% confidence interval for the true population proportion, write your final answer in the form of a sentence! Round to 4 decimal places.
We are 95% confident that the true proportion of weathered pillars is between 27.89% and 57.83%.
Describe the empirical rule. Be specific and clarify what is necessary in order for the rule to work!
The Empirical Rule states that for any bell-shaped (normal) distribution, 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.