Inference & Sampling
A researcher surveys 50 randomly selected students from a school of 2,000 students.
Question: What is the sample?
What is The 50 randomly selected students.
A researcher asks 500 people how many hours they exercise each week.
Question: What type of study is this?
Sample survey.
Which measure represents the center of a data set: mean, median, or IQR?
Mean and median.
In a normal distribution, what percentage of data falls within 1 standard deviation of the mean?
About 68%.
A test score is 85. The mean is 80 and the standard deviation is 5. What is the z-score?
z = 1
A poll finds that 65% of 300 randomly selected voters support a candidate.
Question: What population is the poll trying to describe?
What is All voters in the area being studied.
Scientists assign subjects to receive either a new drug or a placebo.
Question: What type of study is this?
Experiment.
Which measure represents spread: median, mean, or standard deviation?
Standard deviation.
In a normal distribution, what percentage of data falls within 2 standard deviations of the mean?
About 95%.
A basketball player's height is 78 inches. The mean height is 72 inches and the standard deviation is 3 inches. What is the z-score?
z = 2
Why is a random sample preferred over a convenience sample?
A random sample is more likely to represent the population and reduce bias.
Researchers record the diets and health outcomes of people without changing anything.
Question: What type of study is this?
Observational study.
A distribution is heavily skewed.
Question: Which measure of center is most appropriate?
Median.
The mean is 80 and the standard deviation is 5.
Question: What interval contains about 68% of the data?
75 to 85.
A distribution has a mean of 50 and a standard deviation of 10. What data value has a z-score of 1.5?
x = 65
A random sample of 100 students has an average GPA of 3.2.
Question: What inference can be made?
The average GPA of all students is likely close to 3.2.
Why is random assignment important in an experiment?
It helps create similar groups and reduces bias.
Two classes have the same mean score. Class A has a standard deviation of 3 and Class B has a standard deviation of 12.
Question: Which class has more variability?
Class B.
The mean is 70 and the standard deviation is 10.
Question: Approximately what percentage of values are above 90?
About 2.5%.
SAT scores are normally distributed with a mean of 1050 and a standard deviation of 150. What score corresponds to a z-score of -1.2?
x = 870
Two random samples from the same population produce slightly different results.
Question: Why is this expected?
Sampling variability causes different samples to produce different results.
Which study type provides the strongest evidence for cause-and-effect relationships?
A randomized experiment.
Data Set A: Median = 75, IQR = 6
Data Set B: Median = 75, IQR = 18
Question: Which data set is more consistent and why?
Data Set A because it has the smaller IQR.
The mean is 50 and the standard deviation is 4.
Question: Approximately what percentage of values lie between 42 and 58?
About 95% (within 2 standard deviations).
The weights of dogs at a shelter are normally distributed with a mean of 40 lbs and a standard deviation of 8 lbs. Dog A weighs 56 lbs. Dog B weighs 44 lbs. Calculate each dog's z-score and determine which dog is more unusua
Dog A: z = 2
Dog B: z = 0.5
Dog A is more unusual because its z-score is farther from 0.