Collecting Data
What is a population?
The whole set of people or items that are of interest.
What are sampling units?
Individual units of a population
How are outliers represented on box plots?
With a cross or a dot. The end of the affected whisker should then be drawn at the first non-outlier data point, if known – otherwise, at the outlier boundary.
In probability, how do you know if two events are mutually exclusive?
P(A∩B) = 0 (the probability of the intersection is zero)
or P(AUB) = P(A) + P(B).
What is a null hypothesis?
A statement made about a value of the population parameter that we assume to be correct unless there is evidence to suggest otherwise.
What is a census?
A census observes or measures every member of a population.
What is a sampling frame?
List of all sampling units
On a histogram, what goes on the vertical axis?
Frequency density.
When do you use binomial cd
If you want to calculate the probability of a range of values
What notation do we use for the null and alternative hypothesis?
Null hypothesis: Ho
Alternative hypothesis: H1
Name 2 advantages of a census
1) Every single member of population is used
2) It is unbiased
3) Gives an accurate answer
How is a simple random sample taken?
The required elements are chosen at regular intervals from an ordered list.
What do we mean by a casual relationship between variables?
When a change in one variable causes a change on the other. (Correlation does not imply causation so consider the context carefully).
In probability, how do you know if two events are independent?
P(A∩B) = P(A) x P(B) (ie the probability of the intersection is the same as the two probabilities multiplied together).
What is a critical region?
The range of values of the test statistic that would lead us to reject the null hypothesis.
Name 2 disadvantages of a census
1) It takes a long time to do
2) It is costly
3) It is difficult to ensure that the whole population is surveyed
How is quota sampling carried out?
An interviewer or researcher selects a sample that reflects the characteristics of the whole population.
What must you comment on when comparing data sets?
A measure of location and a measure of spread.
Describe and give an example of a discrete uniform distribution.
A discrete uniform distribution is a probability distribution where the
probability of each outcome occurring is the same (e.g rolling a fair die).
What’s an actual significance level, also called the p value?
The probability of incorrectly rejecting the null hypothesis.
Give two circumstances in which it would be necessary to carry out a sample survey rather than a census.
1) If the population is infinite or it’s impossible to obtain all members
2) If the investigation/testing will result in the destruction of the sampling units
How is stratified sampling carried out?
The population is divided into strata and a random sample is taken from each group.
What is the key feature of a histogram? And for what type of data would you use a histogram?
The key feature of a histogram is that the area of each block is proportional to the frequency. We use a histogram for continuous data.
State the four conditions for a Binomial Distribution.
1. There are fixed number of trials.
2. Each trial has two possible outcomes (success/failure).
3. The trials are independent of each other.
4. The probability of success is constant/fixed.
What’s the difference between a one-tailed and two-tailed test?
A one-tailed test looks at either for an increase OR for a decrease in a parameter (ie p>... or p<...), and has a single critical value. A two-tailed test looks for a change in a parameter (ie p ≠...), and has two critical values. For a two tailed test, halve the significance level at the end you’re testing.