Probability
If the chance of finding an empty parking spot in the morning at your high school is 40%, what is the probability that you will find an empty spot?
60% or 0.60
You calculate a 95% Confidence Interval for a local pizza delivery time. If the interval is 20 +- 3 minutes, what is your point estimate and what is the margin of error?
Point estimate 20 minutes; Margin of Error 3 minutes.
In an AP Statistics Hypothesis Test, what does the null hypothesis H0 usually represent?
The status quo, no effect, no difference, or the claim being challenged
You surveyed your friends on their favorite movie genres and want to display the data showing the proportion of each. What is the best graph to use?
A pie chart or a bar graph.
To find out school lunch preferences, you decide to ask every 5th student who enters the cafeteria. What type of sampling method is this?
Systematic random sampling.
You roll a fair, 6-sided die twice in a row. What is the probability of rolling a 6 both times?
1/36 or 0.027
If the margin of error for a poll is 4 percentage points, what sample size change is necessary to cut the margin of error down to 2 percentage points?
You need to multiply the sample size by 4. (Since the margin of error is inversely proportional to root(n), cutting the error in half requires 4 times the n.
A drug trial results in a P-value of (0.012). Using a standard significance level alpha(0.05), what is your statistical decision?
Reject the null hypothesis since (P < alpha)
You weigh a large bag of apples. The distribution of apple weights is heavily skewed to the right. Which is larger: the mean or the median?
The mean is larger (because the high outliers/tail pull the mean toward the right).
You want to know the favorite music genre of students in your grade. You stand outside the band room and ask 50 band students. What type of bias does this introduce?
Voluntary response bias or sampling bias.
At a local coffee shop, 70% of customers buy coffee, 30% buy a pastry, and 20% buy both. What is the probability that a randomly selected customer buys at least one of these items?
80% or 0.80
A poll states the approval rating of the Mayor is 54% with a 3% margin of error. Does this interval provide convincing evidence that the Mayor has the majority support of the town?
Yes, because the entire interval (51% to 57%) is strictly above 50%.
You are testing if a coin is biased. You find a P-value of 0.45. In plain English, what does this P-value mean?
Assuming the coin is fair, there is a 45% chance of getting your observed results (or more extreme) purely by random chance.
A local fast-food restaurant gets an average of 4 drive-thru orders every 15 minutes. What specific probability distribution best models the count of orders during a random 15-minute window?
The Poisson distribution.
A mayor splits the city into its 5 distinct boroughs and randomly selects 500 registered voters from each borough. What sampling method is this?
Stratified random sampling.
A game requires you to draw a specific playing card from a standard 52-card deck and then roll a standard 6-sided die. What is the combined probability of drawing an Ace and rolling an even number?
1/26
You want to estimate the average height of adult golden retrievers to within 1 inch with 95% confidence. The population standard deviation is about 2.5 inches. What is the minimum sample size required?
24 dogs
A factory tests if a new manufacturing method yields fewer defective parts. They fail to reject the null hypothesis, but it turns out the new method actually is better. What type of error did the factory commit?
A Type II Error .
The heights of adult women are approximately normally distributed with a mean of 65 inches and a standard deviation of 3.5 inches. What percentage of women are between 58 and 72 inches tall?
About 95%
A school district wants to survey teachers about a new policy. They randomly select 5 entire schools in the district and survey every single teacher inside those 5 schools. What sampling method is this?
Cluster sampling.
A rapid medical test for a rare disease has a 98% accuracy rate for people with the disease and a 96% accuracy rate for people without it. If 1% of the population has the disease, what is the probability someone who tests positive actually has the disease?
19.8% or 0.198
You create a 95% confidence interval for the average lifespan of a smartphone battery. If the sample standard deviation is 2.5 hours and the sample size is 30, which distribution do you use to find your critical value, and what is the degrees of freedom?
A t-distribution with df = 29. Using a t-distribution because the population standard deviation is unknown.
A medical researcher tests a new heart medication. To minimize the probability of approving an unsafe drug (a severe consequence), should they set their significance level (alpha) to 0.10, 0.05, or 0.01?
alpha = 0.01, because lowering the alpha level decreases the probability of making a Type I Error (falsely concluding it works).
You roll a fair 6-sided die 1,000 times and record the average of your rolls. According to a famous theorem, as your number of rolls increases, what shape will the distribution of these sample means take?
An approximately normal distribution.
You want to survey high schooler's study habits in New York State. Explain how to conduct a simple random sample (SRS) using a numbered roster of every public high school student in the state.
Assign every student a unique number. Use a random number generator (or random digit table) to select students without replacement until your desired sample size is reached.